Trigonometric Identities Question 119
Question: If $ \sin \theta +cosec\theta =2, $ the value of $ {{\sin }^{10}}\theta +cose{c^{10}}\theta $ is
[MP PET 2004]
Options:
A) 10
B) $ 2^{10} $
C) $ 2^{9} $
D) 2
Show Answer
Answer:
Correct Answer: D
Solution:
We have, $ \sin \theta +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 +cose{c^{10}}\theta ={{(1)}^{10}}+\frac{1}{{{(1)}^{10}}}=2 $ .
BETA
