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

|(sin alpha, cos alpha),(cos alpha, -sin alpha)|=

(1+sin alpha)/(1+cos alpha)*(1+sec alpha)/(1+cos ec alpha)=tan alpha

Prove that, (cos alpha + sin alpha)/(cos alpha -sin alpha)-(cos alpha - sin alpha)/(cos alpha + sin alpha) = 2 tan 2 alpha

Prove that, (sin alpha + cos alpha)/(cos alpha-sin alpha)=tan2 alpha + sec 2 alpha

IF tan alpha = ( sin alpha - cos alpha )/( sin alpha + cos alpha) , then sin alpha + cos alpha is

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.

1/(cos alpha + cos 3 alpha)+ 1/(cos alpha + cos 5 alpha)+ 1/(cos alpha + cos 7 alpha) +....+ 1/(cos alpha +cos(2n+1) alpha) = 1/2 "cosec" alpha[tan (n+1) alpha - tan alpha ]

If pi

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