Question

prove : 1+tan^2 A / 1-tan^2 A = sec^2 A

Answer 1

are u sure its right?

Answer 2

yes its written like that.

Answer 3

\[(1+\tan^2 A)/(1-\tan^2 A)\]

Answer 4

oh lols ok wait

Answer 5

i really appreciate your help lalaly.thank you so much.take your time.

Answer 6

\[\sec^2A= 1+\tan^2A\]
\[\tan^2A = \sec^2A-1\]
\[\frac{1+\tan^2A}{1-\tan^2A} = \frac{\sec^2A}{1-(\sec^2A-1)} = \frac{\sec^2A}{\sec^2A} = 1\]
i am sure there is sth wrong here
i checked wolfram too

http://www.wolframalpha.com/input/?i=%281%2Btan^2+A%29+%2F+%281-tan^2+A%29

check ur queation again

Answer 7

you hav to prove it is equal to sec(2A) not sec^2A

Answer 8

1 +tan ² x
= -----------------
1 - tan ² x

1 + sin ² x / cos ² x
= --------------------------
1 -sin ² x / cos ² x

cos ² x +sin ² x
= -------------------
cos ² x - sin ² x

1
= -------------
cos ² x sin ² x

1
= ----------
cos(2x)
= sec(2x)

Answer 9

oh got it man.thanks :) sorry for the late response btw . i just took a shower.

Answer 10

thanks again dude :)