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3.Trigonometrical Ratios, Functions and Identities
easy
જો $\sin \theta + {\rm{cosec}}\theta = 2,$ તો ${\sin ^{10}}\theta + {\rm{cose}}{{\rm{c}}^{10}}\theta $ = . . .
A
$10$
B
${2^{10}}$
C
${2^9}$
D
$2$
Solution
(d) We have, $\sin \theta + {\rm{cosec}}\theta = 2$
$ \Rightarrow $${\sin ^2}\theta + 1 = 2\sin \theta $
$ \Rightarrow $${\sin ^2}\theta – 2\sin \theta + 1 = 0$
$ \Rightarrow $${(\sin \theta – 1)^2} = 0$
$\Rightarrow \sin \theta = 1$ Required value of
${\sin ^{10}}\theta + {\rm{cose}}{{\rm{c}}^{10}}\theta = {(1)^{10}} + \frac{1}{{{{(1)}^{10}}}} = 2$.
Standard 11
Mathematics
