Solve : ` tan^(-1)((cos x)/(1+sin x))`, `-(pi)/(2) lt x lt (pi)/(2)`

Express tan^(-1) ((cos x )/( 1- sin x) ) , ( -3 pi)/(2) lt x lt (pi)/(2) in the simplest form

Simplify tan^(-1).(cosx/(1-sinx))(-pi)/2 lt x lt pi/2

solve: tan^(-1) ((cos x)/(1-sin x)) = ((pi)/(4)+(x)/(2)) , (-3 pi)/(2)ltxlt(pi)/(2)

tan^(-1)(secx+tanx),(-pi)/(2) lt x lt (pi)/(2)

cos^(-1)((sin x+cos x)/(sqrt(2))),(pi)/(4) lt x lt (5pi)/4

Solve : tan^(-1)(sqrt((1-cos x)/(1+cos x))), x lt pi

Express sin^(-1)((sin x+ cos x)/(sqrt2)) , where -(pi)/(4) lt x lt (pi)/(4) , in the simplest form.

Find the simplest form of tan^(-1)(sqrt((1-sin x)/(1+sin x))),0 lt x lt pi

Let f(x) = {{:(-2 sin x,"for",-pi le x le - (pi)/(2)),(a sin x + b,"for",-(pi)/(2) lt x lt (pi)/(2)),(cos x,"for",(pi)/(2) le x le pi):} . If f is continuous on [-pi, pi) , then find the values of a and b.

Solve the following equations : 2tan^(-1) (sin x) = tan^(-1) (2sec x ,) 0 lt x lt pi/2