Trigonometric Identities Question 86

Question: $ (\sec A+\tan A-1)(\sec A-\tan A+1)-2\tan A= $

[Roorkee 1972]

Options:

A) $ \sec A $

B) $ 2\sec A $

C) 0

D) 1

Show Answer

Answer:

Correct Answer: C

Solution:

$ (\sec A+\tan A-1)(\sec A-\tan A+1)-2\tan A $ $ =({{\sec }^{2}}A-{{\tan }^{2}}A)+\sec A+\tan A-\sec A $ $ +\tan A-1-2\tan A=0 $ $ (\because {{\sec }^{2}}A-{{\tan }^{2}}A=1) $