sec^2 theta - tan^2 theta
Answer:
since sec^2 theta = tan^2 theta + 1,
sec^2 theta - tan^2 theta = tan^2 theta + 1 - tan^2 theta
therefore, sec^2 theta - tan^2 theta = 1
sec^2 theta= 1/cos^2(theta) and tan^2 theta= sin^2(theta)/cos^2(theta)
so sec^2 theta - tan^2 theta= 1/cos^2(theta) - sin^2(theta)/cos^2(theta)
=>sec^2 theta - tan^2 theta= (1-sin^theta)/cos^2(theta)
=>sec^2 theta - tan^2 theta= (cos^2 theta)/cos^2(theta)
(b’coz 1-sin^2 theta =cos^2 theta)
=>sec^2 theta - tan^2 theta= 1
