If f (x) = 2(7 cos x + 24 sinx)(7 sinx - 24 cosx), for every x∈R, then maximum value of f(x) is ______ .

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answer is 625.

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Detailed Solution

f(x)=2(7cos⁡x+24sin⁡x)(7sin⁡x−24cos⁡x)Let rcos⁡θ=7;rsin⁡θ=24∴r2=625;tan⁡θ=247∴f(x)=2rcos⁡(x−θ)×rsin⁡(x−θ)=r2(sin⁡2(x−θ))f(x)max=252

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