Which os the following when simplified reduces to unity ? `(1-2sin^2alpha)/(2cot(pi/4+alpha)cos^2(pi/4-alpha))`

The simplified value of sin^(4)alpha+cos^(4)alpha+(1)/(2) sin^(2) 2 alpha is

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

If cos beta is the geometric mean between sin alpha and cos alpha, where 0

If pi

If pi lt alpha lt (3pi)/2 then find the value of expression sqrt(4 sin^4 alpha+ sin^2 2alpha)+ 4 cos^2(pi/4- alpha/2)

If pi lt alpha lt (3pi)/2 then find the value of expression sqrt(4 sin^4 alpha+ sin^2 2alpha)+ 4 cos^2(pi/4- alpha/2)

Simplify be reducing to a single term : sin 3 alpha cos 2 alpha + cos 3 alpha sin 2 alpha.

If pi lt alpha lt 2pi then (1)/(Sin alpha - sqrt(cot^(2)alpha -cos^(2) alpha))=

If pi

Prove that cos (alpha+beta) +sin (alpha-beta)=2sin(pi/4+alpha)cos(pi/4+beta)