`(tan^2alpha-sin^2alpha)*(cot^2alpha)/(sin^2alpha)=`

If a is any real number then :(sin^(4)alpha+sin^(2)alpha*cos^(2)alpha+cos^(2)alpha)/(sin^(2)alpha+sin^(2)alpha*cos^(2)alpha+sin^(2)alpha)=

show that (1-sin^2 alpha)(1-cos^2 alpha)(1+cot^2 alpha)(1+tan^2 alpha) = 1.

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

Prove that, (1+ cos 2 alpha + sin 2 alpha)/(1-cos 2 alpha +sin 2 alpha)=cot alpha

If A=[(cos^2 alpha,sin^2alpha),(cos alpha,sin alpha)] and B=[(sin^2 alpha,cos^2 alpha),(sin alpha,cos alpha)]. Find (A+B).

Prove that: tan(alpha+beta)tan(alpha-beta)=(sin^2 alpha-sin^2 beta)/(cos^2 alpha-sin^2 beta)

(sin^(2)alpha)/(1+cot^(2) alpha) + (tan^(2)alpha)/((1+tan^(2) alpha)^(2)) + cos^(2) alpha =

Prove that: (tan^(3)alpha)/(1+tan^(2)alpha)+(cot^(3)alpha)/(1+cot^(2)alpha)=sec alpha cosec alpha-2sin alpha cos alpha

(1-2sin^(2)alpha)/(1+sin2 alpha)=(1-tan alpha)/(1+tan alpha)

(1-2sin^(2)alpha)/(1+sin2 alpha)=(1-tan alpha)/(1+tan alpha)