3.Trigonometrical Ratios, Functions and Identities
easy

यदि $\sin \theta + {\rm{cosec}}\theta = 2,$ तो ${\sin ^{10}}\theta + {\rm{cose}}{{\rm{c}}^{10}}\theta $ का मान होगा

A

$10$

B

${2^{10}}$

C

${2^9}$

D

$2$

Solution

(d) यहाँ $\sin \theta  + {\rm{cosec}}\theta  = 2$

$ \Rightarrow $${\sin ^2}\theta  + 1 = 2\sin \theta $

$ \Rightarrow $${\sin ^2}\theta  – 2\sin \theta  + 1 = 0$

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

${\sin ^{10}}\theta  + {\rm{cose}}{{\rm{c}}^{10}}\theta $ का अभीष्ट मान

$ = {(1)^{10}} + \frac{1}{{{{(1)}^{10}}}} = 2$.

Standard 11
Mathematics

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