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Question: If \(\cos P = \frac{1}{7}\) and \(\cos Q = \frac{13}{14},\) where P and Q both are acute angles. The...

If cos⁡P=17\cos P = \frac{1}{7} and cos⁡Q=1314,\cos Q = \frac{13}{14}, where P and Q both are acute angles. Then the value of P−QP - Q is

A

30o30^{o}

B

60o60^{o}

C

45o45^{o}

D

75o75^{o}

Answer

60o60^{o}

Explanation

Solution

Given, cos⁡P=17,cos⁡Q=1314\cos P = \frac{1}{7},\cos Q = \frac{13}{14}

∴cos⁡(P−Q)=cos⁡Pcos⁡Q+sin⁡Psin⁡Q\cos(P - Q) = \cos P\cos Q + \sin P\sin Q

=17.1314+487.2714=13+3698=12=cos⁡60o= \frac{1}{7}.\frac{13}{14} + \frac{\sqrt{48}}{7}.\frac{\sqrt{27}}{14} = \frac{13 + 36}{98} = \frac{1}{2} = \cos 60^{o}⇒ P−Q=60oP - Q = 60^{o}.