solve 13-15

​Q13. Prove that tan–1 x =2 tan–1 (cosec tan–1x –tan cos–1x )

Q14. Solve for x : sin–1 x + sin–1 2x –  π 3

Q15. If cos–1 x > sin–1x ,then find x.  

Dear Student,
Please find below the solution to the asked query:

cos-1x>sin-1xBoth sin-1x and cos-1x are defined for x-1,1Now use cos-1x+sin-1x=π2π2-sin-1x>sin-1x2sin-1x<π2sin-1x<π4x<sinπ4x<12Combining x<12 and  x-1,1, we getx[-1,12)

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