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Question
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
Solution
we know sin2A + cos2A = 1
sin2A = 1 – cos2A
= `1 - (15/17)^2`
= `1 - 225/289`
= `(289 - 225)/289`
sin2A = `64/289`
sin A = `+- sqrt(64/289)`
= `+- 8/17`
Since A lies in the first quadrant, sin A is positive
∴ sin A = `8/17`
cos 2A = cos2A – sin2A
= `(15/17)^2 - 64/289`
=`225/289 - 64/289`
= `(225- 64)/289`
= `161/289`
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