Trigonometric Identities

If $\mathrm{sin\theta }=x$, and $\mathrm{cot\theta }=\frac{\sqrt{k-x^2}}{x}$, then find the value of $k$.

$\mathrm{cosec}A=\frac{1}{\sin B}$.

$1-\frac{{\sin }^2\mathrm{A}}{1+\mathrm{cosA}}$

if $\tan \theta =\frac{5}{12}$ find the value of $\frac{3 \cos \theta +5\sin \theta }{3 \cos \theta -5\sin \theta }$

if $\cot \mathrm{\alpha }=\frac{7}{8}$ evaluate $\frac{\left(1+\sin \alpha \right)\left(1-\sin \alpha \right)}{\left(1+\cos \alpha \right)\left(1-\cos \alpha \right)}$

if $\sin A+\mathrm{cosec} A=2$ find the value of ${\sin }^2\mathrm{A}+{\mathrm{cosec}}^2\mathrm{A}$

Given $\text{5 cos A-12 sin A = 0}$ find the value of$\frac{\sin \mathrm{A} + \cos \mathrm{A} }{2 \cos \mathrm{A} - \sin \mathrm{A}}$ 

if $13 \sin A = 5$and $\angle \mathrm{A}$ is acute, find the value of $\frac{5 \sin \mathrm{A} - 2 \cos \mathrm{A} }{\tan \mathrm{A} }$

if $5 \tan \theta = 4,$find the value of $\frac{5 \sin \theta - 3 \cos \theta }{5 \sin \theta + 2 \cos \theta }$

if $\sin \theta =\frac{6}{10}$, find without using tables, the value of $(\cos \theta +\tan \theta )$

if $\sin \theta = \frac{3}{5}$, and $\theta$ is acute angle, find  $\tan \theta$

if $\sin \theta =\frac{3}{5}$, and $\theta$ is acute angle, find  $\cos \theta$

if $2 \sin x = \sqrt{3}$, then evaluate $3 \cos x - 4 {\cos }^{3}x$

if $\frac{\sec \theta - \tan \theta }{\sec \theta + \tan \theta }=\frac{1}{4}$ find $\sin \theta$

if $\tan \theta -\cot \theta = \frac{3}{2}$ find the value of  ${\tan }^2\theta + {\cot }^2\theta$

If $\cos \theta +\sec \theta =\frac{5}{2}$, find the value of ${\cos }^2\theta +{\sec }^2\theta$

In triangle ABC, right angled at B, if  $\tan \mathrm{C} = \sqrt{3}$ find the value of  $\tan \mathrm{A} - \mathrm{Cot} \mathrm{C}$

If $\tan \mathrm{\theta }-\cot \mathrm{\theta }=\frac{3}{2}$, find the value of ${\tan }^2\theta +{\cot }^2\theta$

if $\tan \varphi =\frac{5}{12}$, find the value of  $\frac{(3 \cos \varphi +5 \sin \varphi )}{3 \cos \varphi - 5 \sin \varphi }$

If $\cos \theta =\frac{3}{5}$ , where $‘\theta ’$ is an acute angle. Find the value of $\sin \theta$.