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Question

In any ABC, the simplified form of cos2Aa2-cos2Bb2 is:


A

a2-b2

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B

1a2-b2

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C

1a2-1b2

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D

a2+b2

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Solution

The correct option is C

1a2-1b2


Explanation for the correct option:

Finding the value of the expression:

cos2Aa2-cos2Bb2=1-2sin2Aa2-1-2sin2Bb2bycos2θ=1-2sin2θ=1a2-2sin2Aa2-1b2+2sin2Bb2=1a2-1b2+2sin2Bb2-sin2Aa2=1a2-1b2+20bysinerulesinAa=sinBb=sinCc=1a2-1b2

Hence, option C is correct.


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