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

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3.Trigonometrical Ratios, Functions and Identities

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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

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