Question

Prove that:
sechA (1-cosh^2 A) + coshA (1-sech^2 A) =0​

Answer 1

Explanation:

secA (1-cos²A) + cosA (1-sec²A) = 0

L.H.S.

secA × sin²A + cosA × -tan²A (∵ 1-cos²A = sin²A and -tan²A = 1-sec²A)

sin²A/cosA + cosA × -sin²A/cos²A (∵ secA = 1/cosA and tanA = sinA/cosA

sin²A/cosA - sin²/cosA ( cosA and -sin²A/cos²A here cos²A and cosA get canceled and we get -sin²A/cosA)

(sin²A - sin²A)/cosA

0 =R.H.S.

Please mark as brain list