Question

Express $\tan 68°+\sec 68°$ in terms of trigonometric ratio of angles lying between $0°$ and ${45}^{\circ }$

Answer 1

Finding the value of $\tan 68°+\sec 68°$in terms of the trigonometric ratio:

Given trigonometric expression is $\tan 68°+\sec 68°$.

Trigonometric ratios are:

$\sin A=\cos \left(90°-A\right)$
$\tan A=\cot \left(90°-A\right)$
$\sec A=cosec\left(90°-A\right)$

By using the trigonometric ratio

$\tan 68°=\tan \left(90°-22°\right)=\cot 22°$
$\sec 68°=\sec \left(90°-22°\right)=cosec22°$

Hence, the value of $\tan 68°+\sec 68°=\cot 22°+cosec22°$.