Prove that `tan^(-1)((cosx)/(1+sinx))=(pi/4-x/2)`

1.	Prove that `tan^(-1)((cosx)/(1+sinx))=(pi/4-x/2)`
Answer» We have, LHS `=tan^(-1)(cosx)/(1+sinx)` `=tan^(-1){(sin(pi/2-x))/(1+cos(pi/2-x))}` `=tan^(-1){(2sin(pi/4-x/2)cos(pi/4-x/2))/(2cos^(2)(pi/4-x/2))}` `=tan^(-1){tan(pi/4-x/2)}=(pi/4-x/2)`=RHS. `therefore tan^(-1)((cosx)/(1+sinx))=(pi/4-x/2)`.

Discussion

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