Question

(1-sin²A)/cos²A = 2sec²A-1

Answer 1

Taking L.H.S. = (1-sin^2A) / cos^2A

cos^2A / cos^2A (since, 1 - sin^2A = cos^2A)


1/1 = 1



Now, Taking R.H.S. = 2sec^2A

sec^2 + sec^2A -1 (since, sec^2A+sec^A=2sec^2A)



sec^2A + tan^2A (since, sec^2A-1 = tan^2A)



1 (since, sec^2A + tan^2A = 1)


Therefore, 1 = 1
Hence prove.