Question

if cos^4theta+cos^2theta=1.Find the value of cot^4theta-cot^2theta=1​

Answer 1

Answer:

are we have to prove the equation...?

Step-by-step explanation:

let's take theta as x,

cos⁴x+cos²x=1

cos⁴x=1-cos²x

cos⁴x=sin²x

cos²x=sin²x/cos²x

cos²=tan²x

tan²x . sec²x=1 ....(1)

again,from,

tan²x=cos²x

cot²x=sec²x ....(2)

so, cot⁴x-cot²x

=sec⁴x-sec²x [from eqn. 2]

=sec²x(sec²x-1)

=sec²x tan²x

=1 [from eqn (1)]