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 $\frac{{sin}^{2}3\theta }{{sin}^2\theta }-\frac{{cos}^{2}3\theta }{{cos}^2\theta }$ is equal to

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 ${\prod }_{i=1}^{n}tan{\alpha }_i=1$, where each ${\alpha }_i\in \left[0,\frac{\pi }{2}\right)$, then the maximum value of ${\prod }_{i=1}^{n}sin{\alpha }_i$ is

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

The value of $tan\theta +2tan2\theta +4tan4\theta +8cot8\theta$ is

If $sinx+{sin}^{2}x=1$, then ${cos}^{2}x+{cos}^{4}x$ is equal to

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

If ${sin}^{2}x=1-sinx$, then ${cos}^{4}x+{cos}^{2}x$ 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 $A-B=\frac{\pi }{4}$, then $\left(1+tanA\right)\left(1-tanB\right)$ is equal to

Which of the following is correct?

The value of $sin{30}^{\circ }cos{45}^{\circ }+cos{30}^{\circ }sin{45}^{\circ }$ is

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

The value of $\frac{1-{tan}^2{15}^{\circ }}{1+{tan}^2{15}^{\circ }}$ is

If $sinx$, $cosx$, $tanx$ are in G.P., then ${cot}^{6}x-{cot}^{2}x$ is equal to