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Question

Mathematics Question on Straight lines

∫0π/2cot⁡xcot⁡x+tan⁡xdx is equal to

A

(A) 1

B

(B) -1

C

(C) π2

D

(D) π4

Answer

(D) π4

Explanation

Solution

Explanation:
Let I=∫0π/2cot⁡xcot⁡x+tan⁡xdxNowI=∫0π/2cot⁡(π/2−x)cot⁡(π/2−x)+tan⁡(π/2−x)dx⇒I=∫0π/2tan⁡xcot⁡x+tan⁡xdxOn adding Equations(i) and (ii), we get2I=∫0π/21dx⇒2I=π2⇒I=π4