(1-sin alpha+cos alpha)^(2)=2(1+cos alpha)(1-sin alpha)

Prove the following identities: (1-sin alpha+cosalpha)^2=2(1+cos alpha)(1-sin alpha)

(sin alpha)/(1+cos alpha)+(1+cos alpha)/(sin alpha)=2cosec alpha

If (cos alpha,sin alpha),B(sin alpha,-cos alpha),C(1,2)A(cos alpha,sin alpha),B(sin alpha,-cos alpha),C(1,2) are the vertices of $ABC, then as alpha varies, find the locus of its centroid.

sin alpha-sin2 alpha+sin3 alpha=4cos(3 alpha)/(2)cos alpha sin(alpha)/(2)

If Delta = |(cos alpha,- sin alpha,1),(sin alpha,cos alpha,1),(cos (alpha + beta),- sin (alpha + beta),1)| , then

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

If f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then