Question

Express the following in terms of trigonometric ratios of angles lying between $0^{\circ }$ and ${45}^{\circ }$:
$\cot {85}^{\circ }+\cos {75}^{\circ }$

Answer 1

We know that,

$\cot ({90}^{\circ }-\theta )=\tan \theta$ and

$\cos ({90}^{\circ }-\theta )=\sin \theta$

$\cot {85}^{\circ }=\cot ({90}^{\circ }-5^{\circ })=\tan 5^{\circ }$

$\cos {75}^{\circ }=\cos ({90}^{\circ }-{15}^{\circ })=\sin {15}^{\circ }$

$\therefore \cot {85}^{\circ }+\cos {75}^{\circ }=\tan 5^{\circ }+\sin {15}^{\circ }$