Trigonometric Identities

If $x=a\cos (90°-\theta )$ and $y=b\cot (90°-\theta )$ , then the value of is $\left(\frac{a^2}{x^2}-\frac{b^2}{y^2}\right)$. 

If $\tan \theta =\frac{A}{B}$, What should come in the place of ($?$) for the expression given below?

$\frac{A\sin \theta -B\cos \theta }{A\sin \theta +B\cos \theta }=?$

If $\tan (9°)=\frac{p}{q}$, then find the value of $\frac{{\sec }^2\left(81°\right)}{\left(1+{\cot }^2\left(81°\right)\right)}$.

If $\tan \theta +\sin \theta =p$ and $\tan \theta -\sin \theta =q$, then which of the following is correct?

For all real $A$, then find the simplified value of the expression ${\sin }^{6}A+{\cos }^{6}A+3{\sin }^{2}A {\cos }^{2}A$.

If $\cos x+{\cos }^{2}x=1$, then what should come in the place of ($?$) for the expression given below?

$({\sin }^{12}\left(x\right)+3{\sin }^{10}\left(x\right)+3{\sin }^8\left(x\right)+{\sin }^6\left(x\right)-1)=?$.

If $\sin x+\sin y=a$ and $\cos x+\cos y=a$, then find the value of $\sin x+\cos x$.

The value of $\sin 18º + \cos 36º?$

If $\sec \left(x\right)+\tan \left(x\right)=\sqrt{3}$, then find the positive value of $\sin \left(x\right)$.

If $2y\cos A-x\sin A=0$ and, $2x\left(\sec A\right)-y\left(\mathrm{cosec}A\right)=3$, then find the value of $x^2+4y^2$.

What should come in the place of ($?$) for the expression given below for $n=0$?

$\sin \left((n+1)A\right)·\sin \left((n+2)A\right)+\cos \left((n+1)A\right)·\cos \left((n+2)A\right)=?$

If $\tan \left(\theta \right)=\frac{\sin \left(\mathrm{a}\right)-\cos \left(\mathrm{a}\right)}{\sin \left(\mathrm{a}\right)+\cos \left(\mathrm{a}\right)}$, then find the value of $\sin \left(a\right)+\cos \left(a\right)$.

If $\cos \left(\theta \right)\mathrm{cosec}\left(23°\right) = 1$, then find the value of $\theta$.

$\frac{\tan 3x}{\tan x}$never lies between

What is the value of $\left[\right(1-{\sin }^2 \mathrm{\theta }){\sec }^2 \mathrm{\theta }+{\tan }^2 \mathrm{\theta }]({\cos }^2\mathrm{\theta }+1)$ for $0°<\theta <90°$?

If $\sin x+{\sin }^{2}x+{\sin }^{3}x=1$, then what should come in the place of ($?$) for the expression given below?

 ${\cos }^{6}x-4{\cos }^{4}x+8{\cos }^{2}x=?$

If $\tan \left(A\right)+\sin \left(A\right)=m$ and $\tan \left(A\right)-\sin \left(A\right)=n$, then find the value of $m^2 -n^2$.

If ${\tan }^2\mathrm{\theta }=2{\tan }^2\mathrm{\varphi }+1$ then ${\cos }^2\mathrm{\theta }+{\sin }^2\mathrm{\varphi }$ is equal to:

If$x=a{\cos }^3\theta , y=b{\sin }^3\theta$ , then what should come in the place of ($?$) for the expression given below?

${\frac{x}{a}}^{\frac{2}{3}}+{\frac{y}{b}}^{\frac{2}{3}}=?$

Find the value of $3\sin 15° - 4 {\sin }^3 15°$