Trigonometric Functions & Identities Questions with Solutions

Given that $cos6x=a{cos}^{6}x+b{cos}^{4}x+c{cos}^{2}x+d$ for any real number $x$, find the value of $a+b+c$.

Find the distance from the eye at which a coin of $2cm$ diameter should be held so as to conceal the full moon whose angular diameter is ${31}^{\prime }$.

The number of real solutions of $\sqrt{1+cos2x}=\sqrt{2},{cos}^{-1}(cosx)$ in $\left[\frac{\pi }{2},\pi \right]$ is

The value of the expression $1-\frac{{sin}^{2}y}{1+cosy}+\frac{1+cosy}{siny}-\frac{siny}{1-cosy}$ is equal to

Find the distance from the eye at which a coin of $2cm$ diameter should be held so as to conceal the full moon whose angular diameter is $31\prime$.

The largest value of ${cos}^2\theta -6sin\theta cos\theta +3{sin}^2\theta +2$ is

If $sinx+acosx=b$, then what is the expression for $\left|asinx-cosx\right|$ in terms of a and b?

If $tan\alpha =\frac{m}{m+1}$ and $tan\beta =\frac{1}{2m+1}$, then $\alpha +\beta$ is equal to

If $cos\left(\alpha +\beta \right)=\frac{4}{5}$ and $sin\left(\alpha -\beta \right)=\frac{5}{13}$, where $0<\alpha ,\beta <\frac{\pi }{4}$, then $tan2\alpha$ is equal to

If $tan\theta =\frac{b}{a}$, then the value of $acos2\theta +bsin2\theta$ is

If $sinx$, $cosx$, $tanx$ are in G.P., then ${cot}^{6}x-{cot}^{2}x$ 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 $tan{9}^{\circ }-tan{27}^{\circ }-tan{63}^{\circ }+tan{81}^{\circ }$ is equal to

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