已知tan^2θ=2tan^2α+1,求cos2α-2cos2θ的值I solve the question.who comes,who gets the coins.

Question

已知tan^2θ=2tan^2α+1,求cos2α-2cos2θ的值
I solve the question.who comes,who gets the coins.

Answer 1

数学之美团为你解答
cos(2α) - 2cos(2θ)
= (1 - tan²α) / (1+tan²α) － 2(1 - tan²θ) / (1+tan²θ)
= (1 - tan²α) / (1+tan²α) － 2( - 2 tan²α) / (2+2tan²α)
= (1 - tan²α) / (1+tan²α) + 2tan²α / (1+tan²α)
= (1+tan²α) / (1+tan²α)
= 1