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Question

Let f(x)=∣ ∣cosxsinxcosxcos2xsin2x2cos2xcos3xsin3x3cos3x∣ ∣, then the value of f(π/2)= .....................

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Solution

Given, f(x)=∣ ∣cosxsinxcosxcos2xsin2x2cos2xcos3xsin3x3cos3x∣ ∣
f(x)=∣ ∣sinxcosxsinxcos2xsin2x2cos2xcos3xsin3x3cos3x∣ ∣+∣ ∣cosxsinxcosx2sin2x2cos2x4sin2xcos3xsin3x3cos3x∣ ∣+∣ ∣cosxsinxcosxcos2xsin2x2cos2x3sin3x3cos3x9sin3x∣ ∣
f(π/2)=∣ ∣101102010∣ ∣+∣ ∣010020010∣ ∣+∣ ∣010102309∣ ∣
f(π/2)=1+0+3=4

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