How do you prove tan²(1+cot²)=1/1-sin²?

2 Answers
Feb 27, 2018

Please refer to a Proof in the Explanation.

Explanation:

#tan^2theta(1+cot^2theta)#,

#=tan^2theta+tan^2theta*cot^2theta#,

#=tan^2theta+1#,

#=sec^2theta#,

#=1/cos^2theta#,

#=1/(1-sin^2theta)#.

Feb 27, 2018

See below

Explanation:

#tan2vartheta(1+cot^2vartheta)#

#tan^2vartheta*csc^2vartheta#

#=sin^2vartheta/cos^2vartheta*1/sin^2vartheta#

#=1/cos^2vartheta#

#1/(1-sin^2vartheta)#, as required. #square#