If `sinx=sqrt5/3` and `pi/2 < x < pi,` find the value of (i) `sin\ x/2` (ii) `cos\ x/2` (iii) `tan\ x/2`

Solve |sin 3x + sinx | + |sin 3x - sinx |= sqrt3, - (pi)/(2) lt x lt (pi)/(2).

Solve |sin3x+sinx|+|sin3x-sinx|=sqrt(3), -pi/2 lt theta lt pi/2

simplify cos^(-1) ((sinx+cosx)/sqrt2) , pi/4 < x < (5pi )/4

simplify cos^(-1) ((sinx+cosx)/sqrt2) , pi/4 < x < (5pi )/4

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?

Prove that: cot^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))}=pi/2-x/2 , if pi/2 < x < pi

Show that : int_(0)^(pi/2)sqrt(sinx)/(sqrt(sinx)+sqrt(cosx))dx=pi/4 .

Write the slope of the tangent to the curve y= sqrt3 sinx+cosx at ((pi)/(2),sqrt3) .

If x in (pi, (3pi)/(2)) then int(sqrt(1+sinx)-sqrt(1-sinx))dx=