Basic maths-calculus-Q11

+1 vote

\int cos\text{ } 5x. cos \text{ }3x \text{ }dx

(A) \frac{sin\text{ }8x}{16}+\frac{sin\text{ }2x}{4}

(B) \frac{sin\text{ }8x}{16}-\frac{sin\text{ }2x}{4}

(C) \frac{cos\text{ }8x}{16}-\frac{cos\text{ }2x}{4}

(D) \frac{cos\text{ }8x}{16}+\frac{cos\text{ }2x}{4}

asked May 19 in Basic Maths by gbeditor (44,560 points)
recategorized Jun 9 by deepak-gatebook

1 Answer

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Best answer

cos a *cosb=cos(a+b)+cos(a-b)/2\\ \\ \int cos5x*cos3x=1/2\int cos(5x+3x)+cos(5x-3x)\\ \\ =1/2 \int cos(8x)+cos(2x)\\ \\ =1/2 [(1/8*sin(8x))+1/2*sin(2x)]\\ \\ =sin(8x)/16+sin(2x)/4\\ \\

Therefore answer should be A.

answered May 27 by deepak-gatebook (112,760 points)
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