Question

prove the identity
(1+tan2x)/ (sin2x+cos2x)=sec2x

Answer 1

is it (tanx)^2 or tan(2x)

Answer 2

ok i think its tan(2x)

Answer 3

ok tan(2x)=sin(2x)/cos(2x)

Answer 4

tan2 x

Answer 5

This question came up already, check for spanishkb31

Answer 6

the identity works if the 2s are ^2

Answer 7

multiply both top and bottom by cos(2x)

Answer 8

sin^2(x) + cos^2(x) = 1

Answer 9

so we have [cos(2x)+sin(2x)]/[cos(2x){sin(2x)+cos(2x)}]=1/cos(2x)=sec(2x)

Answer 10

...leaving 1+tan^2(x) = sec^2(x)
which is an identity, but can be further proved by multiplying through by cos^2(x):
sin^2(x) + cos^2(x) = 1

Answer 11

dear god thank you

Answer 12

it doesnt have to be the "squareys"

Answer 13

Haha this is a coincidence. It works in both cases; if 2 is the exponent or part of the angle.

Answer 14

right :)