Trigonometric Ratios & Identities PYQs - Last 5 Years

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Practice 56 MHT CET Mathematics questions from Trigonometric Ratios & Identities. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 5 Years Trigonometric Ratios & Identities Questions

Showing 50 of 56 filtered questions.

1Trigonometric Ratios And Identities

The value of $\cos 15^\circ - \sin 15^\circ$ is ......

2Trigonometric Ratios And Identities

If $x + y = \dfrac{\pi}{4}$, then $(1 + \tan x)(1 + \tan y) =$

3Trigonometric Ratios And Identities

The value of $\cos\left(\dfrac{\pi}{5}\right)$ is ...

4Trigonometric Ratios And Identities

Let $f_k(x) = \dfrac{1}{k}(\cos^k x + \sin^k x)$ where $k \in N$, then $f_6(x) - f_4(x) = \ldots$

5Trigonometric Ratios And Identities

If $\cos 43^\circ + \sin 43^\circ = k^3$, then $\cos 2^\circ = \ldots$

6Trigonometric Ratios And Identities

If $\tan A$ and $\tan B$ are the roots of the equation $5x^2 - 4x + 1 = 0$, then the value of $A + B$ is...

7Trigonometric Ratios And Identities

The value of $\dfrac{\sin^2 3A}{\sin^2 A} - \dfrac{\cos^2 3A}{\cos^2 A}$ is

8Trigonometric Ratios And Identities

The value of $\cos(60^\circ - A)\cdot\cos A\cdot\cos(60^\circ + A)$ is

9Trigonometric Ratios And Identities

If $P = \tan 20^\circ$, then the value of $\dfrac{\tan 160^\circ - \tan 110^\circ}{1 + \tan 160^\circ \tan 110^\circ}$ in terms of $P$, is...

10Trigonometric Ratios And Identities

If $33\theta = \pi$, then the value of $\cos\theta \cos2\theta \cos4\theta \cos8\theta \cos16\theta$ is

11Trigonometric Ratios And Identities

$\tan 105^\circ = $ ......

12Trigonometric Ratios And Identities

If $\cos(\theta-\alpha)=a$ and $\sin(\theta-\beta)=b$, then the value of $\cos^2(\alpha-\beta)+2ab\sin(\alpha-\beta)+\cos^2(\theta-\alpha)$ is...

13Trigonometric Ratios And Identities

The value of the expression $\tan(x - 9\pi)$ is equal to:

14Trigonometric Ratios And Identities

The value of $\cos^2 10^\circ - \cos 10^\circ \cos 50^\circ + \cos^2 50^\circ$ is equal to....

15Trigonometric Ratios And Identities

If $\sin (\alpha+\beta)=1, \sin (\alpha-\beta)=\frac{1}{2}, \alpha, \beta \in\left[0, \frac{\pi}{2}\right]$, then $\tan (\alpha+2 \beta) \cdot \tan (2 \alpha+\beta)=$

16Trigonometric Ratios And Identities

If $0 \leq x \leq \pi$ and $81^{\sin ^2 x}+81^{\cos ^2 x}=30$ Then $x$ takes the value

17Trigonometric Ratios And Identities

If $\sec x+\tan x=2,0 < x < \frac{\pi}{2}$ then $\sin \frac{x}{4}=$

18Trigonometric Ratios And Identities

The maximum value of the function $a \sin x+b \cos x$ is

19Trigonometric Ratios And Identities

\(\cos ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\cos ^4 \frac{7 \pi}{8}=\)

20Trigonometric Ratios And Identities

If $\sin \mathrm{A}+\sin \mathrm{B}=x$ and $\cos \mathrm{A}+\cos \mathrm{B}=y$, then $\sin (A+B)=$

21Trigonometric Ratios And Identities

If $\sin \theta=\frac{1}{2}\left(x+\frac{1}{x}\right)$, then $\sin 3 \theta+\frac{1}{2}\left(x^3+\frac{1}{x^3}\right)=$

22Trigonometric Ratios And Identities

The value of
$$ \begin{aligned} \sin ^2 5^{\circ}+\sin ^2 10^{\circ} & +\sin ^2 15 +\ldots \ldots \ldots \ldots \ldots \ldots+\sin ^2 85^{\circ}+\sin ^2 90^{\circ}= \end{aligned} $$

23Trigonometric Ratios And Identities

If $\sin \mathrm{A}=\mathrm{n} \sin (\mathrm{A}+2 \mathrm{~B})$, then $\tan (\mathrm{A}+\mathrm{B})=$

24Trigonometric Ratios And Identities

If $\mathrm{f}(x)=\cos (\log x)$ then $\mathrm{f}\left(x^2\right) \cdot \mathrm{f}\left(y^2\right)-\frac{1}{2}\left[\mathrm{f}\left(\frac{x^2}{y^2}\right)+\mathrm{f}\left(x^2 y^2\right)\right]$ has the value

25Trigonometric Ratios And Identities

\(3 \tan ^6 10^{\circ}-27 \tan ^4 10^{\circ}+33 \tan ^2 10^{\circ}=\)

26Trigonometric Ratios And Identities

The value of $\tan 20^{\circ} \tan 80^{\circ} \cot 50^{\circ}=$

27Trigonometric Ratios And Identities

If $A+B=\frac{\pi}{2}$ then the maximum value of $\cos \mathrm{A} \cdot \cos \mathrm{B}$ is

28Trigonometric Ratios And Identities

The value of $\sqrt{3} \cot 20^{\circ}-4 \cos 20^{\circ}$ is equal to

29Trigonometric Ratios And Identities

The approximate value of $\cos \left(59^{\circ} 30^{\prime}\right)$ is (given $1^{\circ}=0.0175^{\mathrm{c}}, \sin 60^{\circ}=0.8660$ )

30Trigonometric Ratios And Identities

If $3 \sin \alpha=5 \sin \beta$, then $\tan \left(\frac{\alpha+\beta}{2}\right)+\tan \left(\frac{\alpha-\beta}{2}\right)=$

31Trigonometric Ratios And Identities

If triangle ABC is a right angled at A and $\tan \frac{\mathrm{B}}{2}$, $\tan \frac{\mathrm{C}}{2}$ are roots of the equation $a x^2+b x+c=0$, $\mathrm{a} \neq 0$, then

32Trigonometric Ratios And Identities

If $\tan \mathrm{A}=\frac{1}{\sqrt{x\left(x^2+x+1\right)}}, \tan \mathrm{B}=\frac{\sqrt{x}}{\sqrt{x^2+x+1}}$ and $\tan \mathrm{C}=\sqrt{x^{-1}+x^{-2}+x^{-3}}$ then

33Trigonometric Ratios And Identities

If $\alpha+\beta=\frac{\pi}{2}$ and $\beta+\gamma=\alpha$, then $\tan \alpha$ equals

34Trigonometric Ratios And Identities

The value of the expression $\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}$ is equal to

35Trigonometric Ratios And Identities

If $\mathrm{A}>\mathrm{B}$ and $\tan \mathrm{A}-\tan \mathrm{B}=x$ and $\cot \mathrm{B}-\cot \mathrm{A}=y$, then $\cot (\mathrm{A}-\mathrm{B})=$

36Trigonometric Ratios And Identities

The approximate value of $\cos \left(30^{\circ}, 30^{\prime}\right)$ is given that $1^{\circ}=0.0175^{\circ}$ and $\cos 30^{\circ}=0.8660$

37Trigonometric Ratios And Identities

If $\tan x=\frac{3}{4}$ and $\pi< x< \frac{3 \pi}{2}$, then $\cos \frac{x}{2}=$ ___________

38Trigonometric Ratios And Identities

Let $\alpha$ and $\beta$ be two real roots of the equation $(k+1) \tan ^2 x-\sqrt{2} \lambda \tan x=(1-k)$ where $k(\neq-1)$ and $\lambda$ are real numbers. If $\tan ^2(\alpha+\beta)=50$, then a value of $\lambda$ is

39Trigonometric Ratios And Identities

If $\sin (\theta-\alpha), \sin \theta$ and $\sin (\theta+\alpha)$ are in H.P., then the value of $\cos ^2 \theta$ is

40Trigonometric Ratios And Identities

If $\alpha+\beta+\gamma=\pi$, then the expression $\sin ^2 \alpha+\sin ^2 \beta-\sin ^2 \gamma$ has the value

41Trigonometric Ratios And Identities

The maximum value of $\left(\cos \alpha_1\right) \cdot\left(\cos \alpha_2\right) \ldots .\left(\cos \alpha_n\right)$ under the constraints $0 \leq \alpha_1, \alpha_2, \ldots ., \alpha_n \leq \frac{\pi}{2}$ and $\left(\cot \alpha_1\right) \c...

42Trigonometric Ratios And Identities

The value of $\cos 20^{\circ}+2 \sin ^2 55^{\circ}-\sqrt{2} \sin 65^{\circ}$ is

43Trigonometric Ratios And Identities

The value of $\begin{aligned} \cos \left(18^{\circ}-\mathrm{A}\right) \cos \left(18^{\circ}+\mathrm{A}\right) -\cos \left(72^{\circ}-\mathrm{A}\right) \cos \left(72^{\circ}+\mathrm{A}\right) \text { is equal to }\end{aligned}$

44Trigonometric Ratios And Identities

If $\mathrm{A}+\mathrm{B}=225^{\circ}$, then $\frac{\cot \mathrm{A}}{1+\cot \mathrm{A}} \cdot \frac{\cot \mathrm{B}}{1+\cot \mathrm{B}}$, if it exists, is equal to

45Trigonometric Ratios And Identities

\(\cos ^3\left(\frac{\pi}{8}\right) \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \sin \left(\frac{3 \pi}{8}\right)=\)

46Trigonometric Ratios And Identities

The value of $\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \frac{7 \pi}{8}\right)$ is

47Trigonometric Ratios And Identities

If \(\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}\), then \(\cos ^2 48^{\circ}-\sin ^2 12^{\circ}\) has the value

48Trigonometric Ratios And Identities

If \(\cos 2 B=\frac{\cos (A+C)}{\cos (A-C)}\). Then \(\tan A, \tan B, \tan C\) are in

49Trigonometric Ratios And Identities

If \(\sin (\theta-\alpha), \sin \theta\) and \(\sin (\theta+\alpha)\) are in H.P., then the value of \(\cos 2 \theta\) is

50Trigonometric Ratios And Identities

If \(\mathrm{a} \cos 2 \theta+\mathrm{b} \sin 2 \theta=\mathrm{c}\) has \(\alpha\) and \(\beta\) as its roots, then the value of \(\tan \alpha+\tan \beta\) is