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Question

If cosP=1/7 and cosQ=13/14, where P and Q both are acute angles. Then, the value of PQ is?

A
30o
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B
60o
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C
45o
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D
75o
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Solution

The correct option is B 60o
We are given cosP=17 & cosQ=1314
So, we know thta sin2θ+cos2θ=1
cosθ=1sin2θ or
sinθ=1cos2θ(1)
sinP=1(17)2=1149=48/7
sinQ=1(1314)2=1169196=27/14
let cos(PQ)
=cosPcosQ+sinPsinQ
=17×1314+487×2714
=1398+43×3398
=13+3698=4998=12
PQ=cos1(12)=π3 (as 0<P,Q<π2)
PQ=(π3) or (60o)

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