JEE MainMathematicsEasyCompound angles

The expression
$\cos^{2}(A + B) + \cos^{2}B - 2cos(A + B)cosAcosB$ is

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\cos^{2}(A + B) + \cos^{2}B - 2cos(A + B)cosAcosB

= \cos^{2}(A + B) + \cos^{2}B - cos(A + B)\lbrack(cos(A - B) + cos(A + B)\rbrack

= \cos^{2}B - cos(A - B)cos(A + B)

= \cos^{2}B - (\cos^{2}A - \sin^{2}B) = 1 - \cos^{2}A

Hence it is dependent on A.

Source: Grass-G / M-16 Mathematics Paper 25 Nov First.docx

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