Calculate `tan((alpha)/(2))` if `cos 2 alpha=7/32` and `alpha in (-pi,-(3pi)/(4))`

Calculate cos ((alpha)/(2)) if sin alpha=4/5 and alpha alpha in ((-3pi)/(2),-pi)

Calculate tan alpha if cos alpha =- sqrt(5)/(5) and alpha in (pi (3pi)/(2))

Calculate sin alpha if cos alpha=-9/11 and alpha in (pi,(3pi)/(2))

The expression (sin alpha+cos alpha)/(cos alpha-sin alpha) tan((pi)/(4)+alpha)+1, alpha in (-(pi)/(4), (pi)/(4)) simplifies to :

"If "y=sqrt((2(tanalpha+cotalpha))/(1+tan^(2)alpha)+(1)/(sin^(2)alpha))"when "alpha in ((3pi)/(4),pi)"then find "(dy)/(dalpha)" at"alpha=(5pi)/(6)

tan((pi)/(4)+alpha)=(1+sin2 alpha)/(cos2 alpha)

The expression (1 + sin 2 alpha )/( cos (2 alpha - 2pi) tan (alpha - (3pi)/(4 ))) -1/4 sin 2 alpha [ cot "" (alpha )/(2) + (alpha )/(2))] when simplified reduces to

The number of solutions of the equation tan^(2)alpha-cos es^(2)alpha+4cot^(2)2 alpha+4tan alpha cot2 alpha=0in(0,(pi)/(2))-{(pi)/(4)} is