Trigonometric Identities Question 189
Question: If $ (1+\sin A)(1+\sin B)(1+\sin C) $ $ =(1-\sin A)(1-\sin B)(1-\sin C), $ then each side is equal to
Options:
A) $ \pm \sin A\sin B\sin C $
B) $ \pm \cos A\cos B\cos C $
C) $ \pm \sin A\cos B\cos C $
D) $ \pm \cos A\sin B\sin C $
Show Answer
Answer:
Correct Answer: B
Solution:
Multiplying both sides by $ (1-\sin A)(1-\sin B)(1-\sin C) $ , we have, $ (1-{{\sin }^{2}}A)(1-{{\sin }^{2}}B)(1-{{\sin }^{2}}C) $ $ ={{(1-\sin A)}^{2}}{{(1-\sin B)}^{2}}{{(1-\sin C)}^{2}} $
Þ $ (1-\sin A)(1-\sin B)(1-\sin C)=\pm \cos A\cos B\cos C $ Similarly, $ (1+\sin A)(1+\sin B)(1+\sin C)=\pm \cos A\cos B\cos C $ .
BETA
