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

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

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

cos x-sin x = sqrt (2) cos (x + (pi) / (4))

Let f(x) =sinx + 2 cos^(2)x (pi)/(4)lt=x lt= (3pi)/(4) . Then f attains its

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

if cos x= (-sqrt(15))/(4) " and " (pi)/(2) lt x lt pi find the value of sin x .

If cos x + sin x = a (- (pi)/(2) lt x lt - (pi)/(4)) , then cos 2 x is equal to

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

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0

If sec x cos 5x=-1 and 0 lt x lt (pi)/(4) , then x is equal to