Trigonometric Functions & Identities Questions with Solutions

If $A={cos}^2\theta +{sin}^4\theta$, then for all values of $\theta$:

The maximum value of $\left(cos{\alpha }_1\right)\left(cos{\alpha }_2\right)\cdots \left(cos{\alpha }_n\right)$, where $0\le {\alpha }_1,{\alpha }_2,\dots ,{\alpha }_n\le \pi$ and $\left(cot{\alpha }_1\right)\left(cot{\alpha }_2\right)\cdots \left(cot{\alpha }_n\right)=1$, is

If $cos\alpha +cos\beta =a$, $sin\alpha +sin\beta =b$ and $\theta$ is the arithmetic mean between $\alpha$ and $\beta$, then $sin2\theta +cos2\theta$ is equal to

If $\left(1+tan{1}^{\circ }\right)\left(1+tan{2}^{\circ }\right)\cdots \left(1+tan{45}^{\circ }\right)=2^n$, then the value of $n$ is

The value of $sin{12}^{\circ }sin{48}^{\circ }sin{54}^{\circ }$ is

The expression $\frac{tanA}{1-cotA}+\frac{cotA}{1-tanA}$ can be written as

If $3sinx+4cosx=5$, then $6tan\frac{x}{2}-9{tan}^2\frac{x}{2}=$

If $\frac{tanx}{2}=\frac{tany}{3}=\frac{tanz}{5}$ and $x+y+z=\pi$, then the value of ${tan}^{2}x+{tan}^{2}y+{tan}^{2}z$ is

Find the value of $sin{12}^{\circ }sin{48}^{\circ }sin{54}^{\circ }$

The value of $sin{10}^{\circ }sin{50}^{\circ }sin{70}^{\circ }$ is

The value of $tan{9}^{\circ }-tan{27}^{\circ }-tan{63}^{\circ }+tan{81}^{\circ }$ is equal to

If $acos\theta +bsin\theta =2$ and $asin\theta -bcos\theta =3$, then $a^2+b^2=$

If $cosec\theta -cot\theta =2$, then the value of $cosec\theta$ is

If $a_1,a_2,a_3,\dots ,a_n$ are in arithmetic progression with common difference $d$, then the sum $sind\left(cosec{a}_{1}cosec{a}_2+cosec{a}_{2}cosec{a}_3+\dots +cosec{a}_{n-1}cosec{a}_n\right)$ is equal to

The value of $tan{1}^{\circ }tan{2}^{\circ }tan{3}^{\circ }\cdots tan{89}^{\circ }$ is:

If $sinx+acosx=b$, then $\left|asinx-cosx\right|$ is:

In a right-angled triangle, the hypotenuse is four times the perpendicular drawn to it from the opposite vertex. The value of one of the acute angles is

The value of $tan\left(\frac{7\pi }{8}\right)$ is

If $tanx=-\frac{3}{4}$ and $\frac{3\pi }{2}<x<2\pi$, then the value of $sin2x$ is

If $cos\theta =\frac{4}{5}$ and $cos\varphi =\frac{12}{13}$, $\theta$ and $\varphi$ both in the fourth quadrant, the value of $cos\left(\theta +\varphi \right)$ is