If `y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")),`prove that `siny=tan^2x/2`

If `y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")),`prove that `siny=

1.	If `y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")),`prove that `siny=tan^2x/2`
Answer» `y= cot^-1 sqrt(cos x) - tan^-1 sqrt cosx` `y = cot^-1 sqrtcosx - tan^-1 sqrt cos x ` `= tan^-1 sqrt secx - tan^-1 sqrt cos x` `y = tan^-1 ((sqrt secx - sqrt cos x)/(1+1)) ` `= tan^-1 ( (sqrt secx - sqrt cosx)/2)` `y= tan^-1 ((1 -cosx)/(2 sqrtcosx))` `tan y = (1- cosx)/(2 sqrt cosx)` now, `sin y = (1 -cosx)/ (1+cosx) ` `= (2sin^2 (x/2))/(2 cos^2(x/2))= tan^2 (x/2)` Answer

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