Value of sin 15^{circ}

English

Gujarati

Hindi

3.Trigonometrical Ratios, Functions and Identities

easy

Find the value of $\sin 15^{\circ}$

A

$\frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}$

B

$\frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}$

C

$\frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}$

D

$\frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}$

Solution

We have

$\sin {15^\circ } = \sin \left( {{{45}^\circ } – {{30}^\circ }} \right)$

$ = \sin {45^\circ }\cos {30^\circ } – \cos {45^\circ }\sin {30^\circ }$

$ = \frac{1}{{\sqrt 2 }} \times \frac{{\sqrt 3 }}{2} – \frac{1}{{\sqrt 2 }} \times \frac{1}{2} = \frac{{\sqrt 3 – 1}}{{2\sqrt 2 }}$

Standard 11

Mathematics

Share

Similar Questions

If $\sin \theta = \frac{{24}}{{25}}$ and $\theta $ lies in the second quadrant, then $\sec \theta + \tan \theta = $

easy

If $x{\sin ^3}\alpha + y{\cos ^3}\alpha = \sin \alpha \cos \alpha $ and $x\sin \alpha – y\cos \alpha = 0,$ then ${x^2} + {y^2} = $

medium

If $x + \frac{1}{x} = 2\cos \alpha $, then ${x^n} + \frac{1}{{{x^n}}} = $

easy

If $5\tan \theta = 4,$ then $\frac{{5\sin \theta – 3\cos \theta }}{{5\sin \theta + 2\cos \theta }} = $

easy

The minute hand of a watch is $1.5 \,cm$ long. How far does its tip move in $40$ minutes? ( Use $\pi=3.14$ ).

medium