Trigonometric Ratios of Complementary Angles

In the figure, find the value of $\sin \left(90-\theta \right)$ and $\tan \alpha$.

Evaluate: $\frac{\tan 65°}{\cot 25°}+\frac{\sin {\displaystyle }{\displaystyle 25}{\displaystyle °}}{\cos {\displaystyle }{\displaystyle 65}{\displaystyle °}}$

If $A+B=90°$, prove that:

$\frac{\cos A}{1+\cos B}+\frac{1+\cos B}{\cos A}=\frac{2}{\cos A}$

If $A+B=90°$,  prove that 

$\frac{\cos A}{1+\cos B}+\frac{1+\cos B}{\cos A}=\frac{2}{\cos A}$ 

If $\theta$ is a positive acute angle and $\sin 3\theta =\cos \left(2\theta +15°\right)$, then find the value of $\theta$ in degree.

If $\theta$ is an acute angle and $\sin 10\theta =\cos \left(5\theta -15°\right)$, then find the value of $\theta$ in degree $\left(°\right)$.

Find the value of $\tan 2A$, if $\cos 3\mathrm{A}=\sin 45°$.

Write the value of $\cos 50°.cosec40°$

Evaluate: $cosec 39°·\sec 51°-\tan 51°·\cot 39°$.

Evaluate: $\frac{\tan 65°}{\cot 25°}$

If $\tan A=\cot B$, then find $A+B$.

Express the following in terms of trigonometric ratios of angle between $0°$ and $90°$.

$\tan 68°+\sec 68°$

Express the following in terms of trigonometric ratios of angle between $0°$ and $90°$

$\sin 81°+\sin 71°$

Find the value of $\tan 5°\tan 25°\tan 30°\tan 45°\tan 65°\tan 85°$.

Find the value of $\cot 12°\cot 38°\cot 52°\cot 60°\cot 78°$

Find the value of ${\left(\frac{\sin 27°}{\cos 63°}\right)}^2+{\left(\frac{\cos 63°}{\sin 27°}\right)}^2$

Find the value of ${\left(\frac{\sin 35°}{\cos 55°}\right)}^2+\left(\frac{\cos 55°}{\sin 35°}\right)-2\cos 60°$

Find the value of $\sin {70}^{°}\sin {20}^{°}-\cos {20}^{°}\cos {70}^{°}$

Find the value of the expression $\sin \theta \cos \left(90-\theta \right)+\cos \theta \sin \left(90-\theta \right)$.

Find the value of $\frac{\sin 36°}{\cos 54°}-\frac{\sin {\displaystyle 54°}}{\cos {\displaystyle 36°}}$