Inverse Trigonometric Functions Question 13
Question: If $ {{\sin }^{-1}}x=\theta +\beta $ and $ {{\sin }^{-1}}y=\theta -\beta , $ then $ 1+xy= $
Options:
A) $ {{\sin }^{2}}\theta +{{\sin }^{2}}\beta $
B) $ {{\sin }^{2}}\theta +{{\cos }^{2}}\beta $
C) $ {{\cos }^{2}}\theta +{{\cos }^{2}}\beta $
D) $ {{\cos }^{2}}\theta +{{\sin }^{2}}\beta $
Show Answer
Answer:
Correct Answer: B
Solution:
Obviously $ x=\sin (\theta +\beta ) $ and $ y=\sin (\theta -\beta ) $
$ \therefore 1+xy=1+\sin (\theta +\beta )\sin (\theta -\beta ) $
$ =1+{{\sin }^{2}}\theta -{{\sin }^{2}}\beta ={{\sin }^{2}}\theta +{{\cos }^{2}}\beta $ .
BETA
