Question

if sectheta + tantheta =L then prove that sectheta=L square +1 /2L

Answer 1

Sec theta + tan theta =L -----(1)
Sec sqare theta - tan square theta = 1
(Sec theta + tan theta) (sec theta - tan theta) =1
Sec theta - tan theta =1 / (sec theta + tan theta)
Sec theta - tan theta = 1 / L -----(2)
(1) + (2) ----) 2 sec theta = L + 1 / L
-----) sec theta = 1 / 2 (L + 1 / L)
-----) sec theta = L square + 1/L
Hence proved