If sin x + {rm{cosec}},x = 2, then sin^n x + cosec^n x is equal to

English

Gujarati

Hindi

3.Trigonometrical Ratios, Functions and Identities

easy

If $\sin x + {\rm{cosec}}\,x = 2,$ then $sin^n x + cosec^n x$ is equal to

A

$2$

B

${2^n}$

C

${2^{n - 1}}$

D

${2^{n - 2}}$

Solution

(a) $\sin x + \cos {\rm{ec}}x = 2$

$\Rightarrow {(\sin x – 1)^2} = 0 \Rightarrow \sin x = 1$

$\therefore {\sin ^n}x + {\rm{cose}}{{\rm{c}}^n}x = 1 + 1 = 2$ .

Standard 11

Mathematics

Share

Similar Questions

Find the degree measures corresponding to the following radian measures ( Use $\pi=\frac{22}{7}$ ).

$\frac{7 \pi}{6}$

easy

If in two circles, arcs of the same length subtend angles $60^{\circ}$ and $75^{\circ}$ at the centre, find the ratio of their radii.

medium

$\tan 1^\circ \tan 2^\circ \tan 3^\circ \tan 4^\circ ……..\tan 89^\circ = $

easy

If $\sin \theta + \cos \theta = 1$, then $\sin \theta \cos \theta = $

easy

If the arcs of the same length in two circles $S_1$ and $S_2$ subtend angles $75^o $ and $120^o $ respectively at the centre. The ratio $\frac{{{S_1}}}{{{S_2}}}$ is equal to

normal