What is `(dsqrt(1 - sin 2x))/dx` equal to, where `pi/4 lt x lt pi/2` ?

What is (dsqrt(1-sin2x))/dx equal to, where pi/4ltxltpi/2 ?

Evaluate int tan^(-1) { sqrt((1-sin x)/(1+ sin x ))} dx , -pi/2 lt x lt pi/2

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

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

If y=tan^(-1) [(sqrt(1+sinx)-sqrt(1-sin x))/(sqrt(1+sin x)+sqrt(1-sin x)]] where 0 lt x lt pi/2 find (dy)/(dx)

Principal solutions of the equation sin 2x + cos 2x =0 . Where pi lt x lt 2pi are

What is the sign of cos( x/2) – sin(x/2) when (i) 0lt x lt pi/4 (ii) (pi)/(2)lt xlt pi

If sin x=(12)/(13) "and sin " y= (4)/(5) " where " (pi)/(2) lt x lt pi " and " 0 lt y lt .(pi)/(2) find the values of (i) " sin " (x+y) " "(ii) " cos " (x+y) " "(iii) " tan " (x-y)

If sinx=(1)/(sqrt5).siny=(1)/(sqrt(10)) , where 0 lt x lt (pi)/(2),0 lt y lt (pi)/(2) , then what is (x+y) equal to?