Question

Differentiate tan inverse cos x/1+sinx with respect to x​

Answer 1

plz refer to the attachment (◔‿◔)

Answer 2

Answer:

tan−1(1+cosxsinx)tan−1⁡(1+cos⁡xsin⁡x)

=tan−1(1+2cos2x2−12sinx2cosx2)=tan−1⁡(1+2cos2⁡x2−12sin⁡x2cos⁡x2)

=tan−1(2cos2x22sinx2cosx2)=tan−1⁡(2cos2⁡x22sin⁡x2cos⁡x2)

=tan−1(cosx2sinx2)=tan−1⁡(cos⁡x2sin⁡x2)

=tan−1(cotx2)=tan−1⁡(cot⁡x2)

=tan−1(tan(π2−x2))=tan−1⁡(tan⁡(π2−x2))

=π2−x2