Question

what is value of cosec 15 ?

Answer 1

cosec15=1/sin15
sin15=sin (45-30)
=sin45cos30-cos45sin30
=1/root2×root3/2-1/root2×1/2
=root3/2root2-1/2root2
=root3-1/2root2.....

hope it will help you ☺

Answer 2

Answer:

$\text{The value of }\cosec 15^{\circ}\text{ is }\frac{\sqrt3+1}{2\sqrt2}$

Step-by-step explanation:

we have to find the value of cosec 15°

$cosec \theta=\frac{1}{\sin \theta}$

∴ $cosec 15^{\circ}=\frac{1}{\sin15^{\circ}}$

$\sin 15^{\circ}=\sin(45-30)^{\circ}$

By trigonometric identity

$\sin(x-y)=\sin x \cos y-\cos x \sin y$

$=\sin 45^{\circ}\cos 30^{\circ}-\cos45^{\circ}\sin30^{\circ}$

$=\frac{1}{\sqrt2}\times \frac{\sqrt3}{2}-\frac{1}{\sqrt2}\times \frac{1}{2}$

$=\frac{\sqrt3}{2\sqrt2}-\frac{1}{2\sqrt2}$

$=\frac{\sqrt3+1}{2\sqrt2}$