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Find maximum value of ( 5 cos thetha - 12 cos thetha )× ( 5 cos thetha + 12 sin thetha

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Find maximum value of ( 5 cos θ - 12 cos θ )× ( 5 cos θ + 12 sin θ)

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(5cosθ - 12sinθ)(5cosθ+12sinθ)

= 25cos2θ - 144sin2θ

= 25cos2θ - 144 (1 - cos2θ)

= 25cos2θ + 144cos2θ - 144

= 169cos2θ - 144

Since,

Maximum value of cos2θ is 1.

Hence,

Maximum value = 169 - 144 = 25

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