Trigonometric Identities Question 36
Question: If $ \cos P=\frac{1}{7} $ and $ \cos Q=\frac{13}{14}, $ where P and Q both are acute angles. Then the value of $ P-Q $ is
[Karnataka CET 2002]
Options:
A) $ 30^{o} $
B) $ 60^{o} $
C) $ 45^{o} $
D) $ 75^{o} $
Show Answer
Answer:
Correct Answer: B
Solution:
Given, $ \cos P=\frac{1}{7},\cos Q=\frac{13}{14} $ \ $ \cos (P-Q)=\cos P\cos Q+\sin P\sin Q $ $ =\frac{1}{7}.\frac{13}{14}+\frac{\sqrt{48}}{7}.\frac{\sqrt{27}}{14}=\frac{13+36}{98}=\frac{1}{2}=\cos 60^{o} $
Þ $ P-Q=60^{o} $ .
BETA
