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Question

If cosP=17 and cosQ=1314 where P and Q both are acute angles.

Then the value of P-Q is


A

30°

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B

60°

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C

45°

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D

75°

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Solution

The correct option is B

60°


Step 1. Find the value of P-Q:

Given, cosP=17

sinP=1149 sin2A+cos2A=1

=4849=487

Similarly,

cosQ=1314

sinQ=1169196

=27196=2714

Step 2. Put the values of cosP,sinP,cosQ,sinQ in given expression, we get

cos(PQ)=cosPcosQ+sinPsinQ=171314+4872714=1398+3698=(13+36)98=4998=12

P-Q=cos-112=60°

Hence, Option ‘B’ is Correct.


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