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NCERT Class XII Mathematics Chapter - - Solutions

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Find the following integrals in Exercises 6 to 20.
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Question : 19 of 271
Marks: +1, -0
∫sec⁡2xcsc⁡2xdx\int\frac{\sec^2x}{\csc^2x}dx
Solution:  
Let I=∫sec⁡2xcsc⁡2xdxI=\int\frac{\sec^2x}{\csc^2x}dx
=∫1cos⁡2x⋅sin⁡2xdx=\int\frac{1}{\cos^2x}\cdot\sin^2x dx
=∫tan⁡2xdx=\int\tan^2x dx
=∫(sec⁡2x−1)dx=\int(\sec^2x-1)dx
=tan⁡x−x+C=\tan x-x+C
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