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

tan ^(-1)(cos sqrt(x))

If u= cot ^(-1) (sqrt(cos 2 theta)) -tan ^(-1)(sqrt(cos 2 theta)) , then prove that : sin u = tan^(2) theta .

y=tan^(-1)(x/(1+sqrt(1-x^2)))

y=tan^(-1)(x/(1+sqrt(1-x^2)))

y=tan^(-1)(x/(1+sqrt(1-x^2)))

(v) tan^(-1)sqrt((1+cos x)/(1-cos x))

If intsqrt(cos e cx+1)dx=kfog(x)+c ,w h e r ek is a real constant, then (a). k=-2,f(x)=cot^(-1)x ,g(x)=sqrt(cos e cx-1) (b) k=-2,f(x)=tan^(-1)x ,g(x)=sqrt(cos e cx-1) (c) k=2,f(x)=tan^(-1)xg(x)=(cotx)/(sqrt(cos e cx-1)) (d) k=2,f(x)=cot^(-1)xg(x)=(cotx)/(sqrt(cos e cx-1))

Prove that : (1)/(2) cos^(-1) ((1+ 2 cos x)/( 2+cosx) ) = tan^(-1) ((1)/(sqrt(3)) "tan" (x)/(2))

If tan^(-1).(a+x)/(a) + tan ^(-1) ((a-x)/(a)) = (pi)/(6) then prove that x^(2) = 2sqrt(3)a^(2)

If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha , then x^2= sin2\ alpha (b) sin\ alpha (c) cos2\ alpha (d) cos\ alpha