Trigonometric Ratios & Identities · Mathematics · MHT CET

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MCQ (Single Correct Answer)

MHT CET 2024 16th May Evening Shift
The value of $\cos 20^{\circ}+2 \sin ^2 55^{\circ}-\sqrt{2} \sin 65^{\circ}$ is
MHT CET 2024 16th May Morning Shift
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 \al...
MHT CET 2024 15th May Evening Shift
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...
MHT CET 2024 15th May Morning Shift
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)...
MHT CET 2024 11th May Morning Shift
$$ \cos ^3\left(\frac{\pi}{8}\right) \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \sin \left(\frac{3 \pi}{8}\right)=$$
MHT CET 2024 9th May Morning Shift
If $\alpha+\beta=\frac{\pi}{2}$ and $\beta+\gamma=\alpha$, then $\tan \alpha$ equals
MHT CET 2024 4th May Evening Shift
If $\mathrm{A}>\mathrm{B}$ and $\tan \mathrm{A}-\tan \mathrm{B}=x$ and $\cot \mathrm{B}-\cot \mathrm{A}=y$, then $\cot (\mathrm{A}-\mathrm{B})=$...
MHT CET 2024 4th May Morning Shift
The value of the expression $\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}$ is equal to
MHT CET 2024 3rd May Evening Shift
If $\sin (\theta-\alpha), \sin \theta$ and $\sin (\theta+\alpha)$ are in H.P., then the value of $\cos ^2 \theta$ is
MHT CET 2024 3rd May Evening Shift
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 nu...
MHT CET 2024 3rd May Morning Shift
If $\tan x=\frac{3}{4}$ and $\pi
MHT CET 2024 3rd May Morning Shift
The approximate value of $\cos \left(30^{\circ}, 30^{\prime}\right)$ is given that $1^{\circ}=0.0175^{\circ}$ and $\cos 30^{\circ}=0.8660$
MHT CET 2024 2nd May Evening Shift
If $\alpha+\beta+\gamma=\pi$, then the expression $\sin ^2 \alpha+\sin ^2 \beta-\sin ^2 \gamma$ has the value
MHT CET 2023 14th May Evening Shift
If $$\mathrm{a} \cos 2 \theta+\mathrm{b} \sin 2 \theta=\mathrm{c}$$ has $$\alpha$$ and $$\beta$$ as its roots, then the value of $$\tan \alpha+\tan \b...
MHT CET 2023 14th May Morning Shift
If $$\sin (\theta-\alpha), \sin \theta$$ and $$\sin (\theta+\alpha)$$ are in H.P., then the value of $$\cos 2 \theta$$ is
MHT CET 2023 13th May Morning Shift
The value of $$\begin{aligned} \cos \left(18^{\circ}-\mathrm{A}\right) \cdot \cos ( & \left.18^{\circ}+\mathrm{A}\right) \\ & -\cos \left(72^{\circ}-\...
MHT CET 2023 12th May Evening Shift
$$\cos ^2 48^{\circ}-\sin ^2 12^{\circ}=$$ _________, if $$\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$$
MHT CET 2023 12th May Morning Shift
If $$\tan \theta=\frac{\sin \alpha-\cos \alpha}{\sin \alpha+\cos \alpha}, 0 \leq \alpha \leq \frac{\pi}{2}$$, then the value of $$\cos 2 \theta$$ is...
MHT CET 2023 11th May Morning Shift
The value of $$\tan \left(\frac{\pi}{8}\right)$$ is _________.
MHT CET 2023 10th May Morning Shift
The value of $$\tan \frac{\pi}{8}$$ is
MHT CET 2023 9th May Evening Shift
If $$\cos 2 B=\frac{\cos (A+C)}{\cos (A-C)}$$. Then $$\tan A, \tan B, \tan C$$ are in
MHT CET 2023 9th May Morning Shift
If $$\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$$, then $$\cos ^2 48^{\circ}-\sin ^2 12^{\circ}$$ has the value
MHT CET 2022 11th August Evening Shift
If $$\cot (A+B)=0$$, then $$\sin (A+2 B)$$ is equal to
MHT CET 2021 24th September Evening Shift
$$\tan \mathrm{A}+2 \tan 2 \mathrm{~A}+4 \tan 4 \mathrm{~A}+8 \cot 8 \mathrm{~A}=$$
MHT CET 2021 24th September Morning Shift
If $$a \sin \theta=b \cos \theta$$, where $$a, b \neq 0$$, then $$a\cos 2 \theta+b \sin 2 \theta=$$
MHT CET 2021 23rd September Evening Shift
If $$\sin (y+z-x), \sin (z+x-y)$$ and $$\sin (x+y-z)$$ are in AP, then
MHT CET 2021 22th September Evening Shift
If $$2 \cos \theta=x+\frac{1}{x}$$, then $$2 \cos 3 \theta=$$
MHT CET 2021 22th September Morning Shift
$$\tan 3 \mathrm{~A} \cdot \tan 2 \mathrm{~A} \cdot \tan \mathrm{A}=$$
MHT CET 2021 21th September Morning Shift
If $$\frac{\cos (A+B)}{\cos (A-B)}=\frac{\sin (C+D)}{\sin (C-D)}$$, then $$\tan A \tan B \tan C=$$
MHT CET 2021 20th September Evening Shift
If $$\cos x=\frac{24}{25}$$ and $$x$$ lięs in first quadrant, then $$\sin \frac{x}{2}+\cos \frac{x}{2}=$$
MHT CET 2021 20th September Morning Shift
The value of $$\sin 18^{\circ}$$ is
MHT CET 2020 19th October Evening Shift
$$\frac{1-\sin \theta+\cos \theta}{1-\sin \theta-\cos \theta}=$$
MHT CET 2020 19th October Evening Shift
If $A$ and $B$ are supplementary angles, then $\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}=$
MHT CET 2020 16th October Evening Shift
$$\begin{aligned} & \cos \left(36^{\circ}-A\right) \cos \left(36^{\circ}+A\right)+\cos \left(54^{\circ}+A\right) \cos \\ & \left(54^{\circ}-A\right)= ...
MHT CET 2020 16th October Evening Shift
If $$x+y=\frac{\pi}{2}$$, then the maximum value of $$\sin x \cdot \sin y$$ is
MHT CET 2020 16th October Evening Shift
If $$a=\sin 175^{\circ}+\cos 175^{\circ}$$, then
MHT CET 2020 16th October Morning Shift
The polar co-ordinates of the point whose cartesian co-ordinates are $$(-2,-2)$$, are given by
MHT CET 2020 16th October Morning Shift
If $$x \cos \theta+y \sin \theta=5, x \sin \theta-y \cos \theta=3$$, then the value of $$x^2+y^2=$$
MHT CET 2020 16th October Morning Shift
If $$\sin \theta=-\frac{12}{13}, \cos \phi=-\frac{4}{5}$$ and $$\theta, \phi$$ lie in the third quadrant, then $$\tan (\theta-\phi)=$$
MHT CET 2019 3rd May Morning Shift
$$\frac{1-2\left[\cos 60^{\circ}-\cos 80^{\circ}\right]}{2 \sin 10^{\circ}}=\ldots \ldots$$
MHT CET 2019 2nd May Evening Shift
The value of $\sin 18^{\circ}$ is $\qquad$
MHT CET 2019 2nd May Morning Shift
If $\theta=\frac{17 \pi}{3}$ then, $\tan \theta-\cot \theta=\ldots$
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