Inverse Trigonometric Functions Question 126
Question: If $ {{\tan }^{-1}}(sin^{2}\theta -2sin\theta +3)+co{t^{-1}}({5^{{{\sec }^{2}}y}}+1)=\frac{\pi }{2} $ , then the value of $ {{\cos }^{2}}\theta -\sin \theta $ is equal to
Options:
A) 0
B) -1
C) 1
D) none of these
Show Answer
Answer:
Correct Answer: C
From the given equation $ {{\sin }^{2}}\theta -2\sin \theta +3={5^{{{\sec }^{2}}y}}+1 $ , we get $ {{(sin\theta -1)}^{2}}+2={5^{{{\sec }^{2}}y}}+1 $
$ L\text{.}H.S.\le 6,R.H.S.\ge 6 $
Possible solution is $ \sin \theta =-1 $ when L.H.S. = R.H.S.
$ \Rightarrow {{\cos }^{2}}\theta =0 $
$ \Rightarrow {{\cos }^{2}}\theta -\sin \theta =1 $
BETA
