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

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

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

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

Prove: (2)/( cot alpha tan 2 alpha ) = 1 - tan ^(2) alpha.

If cot^(-1)(sqrt(cos alpha))-tan^(-1)(sqrt(cos alpha))=x then sin x is tan^(2)(alpha)/(2)(b)cot^(2)(alpha)/(2)(c)tan^(2)alpha(d)cot(alpha)/(2)

Prove that sin 4alpha = 4 tan alpha (1 - tan^(2) alpha)/((1 + tan^(2) alpha)^(2))

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

If cos^(2)alpha-sin^(2)alpha=tan^(2)alpha, then show that tan^(2)alpha=cos^(2)beta-sin^(2)beta