Question

Math Analysis: Prove the given identity
tan^2 x - sin^2 x = tan^2 x sin^2 x

Answer 1

ohh rewrite Tan in terms of sines and cosines and do some algebra.

Answer 2

thx but im still confused..

Answer 3

Tan = Sin/Cos
Tan^2 = (Sin/Cos)^2

Answer 4

(Sin/Cos)^2 - Sin^2 = (Sin/Cos)^2 * Sin^2

Answer 5

They're asking if that's true.

Answer 6

i got that, this is what I got
sin^2 x/cos^2 x - sin^2 x*cos^2 x/cos^2 x
sin^2 x/cos^2 x - sin^2 x*cos^2 x/cos^2 x

Answer 7

why would you multipy sin^2 x/cos^2 x by sin^2 x?

Answer 8

sin^x(1-cos^2x)/cos^2x

Answer 9

sin^2 x/cos^2 x - sin^2 x*cos^2 x/cos^2 x
->
sin^x(1-cos^2x)/cos^2x

Answer 10

Yea, well basically u get:
(Sin^2 - Sin^2*Cos^2)/Cos^2 on the left. Simplify a little:
Sin^2(1-Cos^2)/Cos^2

Sin^2+Cos^2=1, so 1-Cos^2= Sin^2

Answer 11

So it simplifies to:
Sin^2*Sin^2/Cos^2, or Sin^4/Cos^2

Answer 12

the answer to the equation is tan^2 x*sin^2 x

Answer 13

Right side: tan^2/Sin^2 = (Sin/Cos)^2/(Sin^2)

Answer 14

sin^2 x/cos^2 x - sin^2 x*cos^2 x/cos^2 x
->
sin^2x(1-cos^2x)/cos^2x
# 1-cos^2x=sin^2x
so, sin^2x*sin^2x/cos^2x
-> tan^2x*sin^2x

Answer 15

@iawanbahyudin where did the sin^2 x(1-cos^2 x)/cos^2 x come from?

Answer 16

nvm i got it thx for the help! =)

Answer 17

sin^2 x/cos^2 x - sin^2 x*cos^2 x/cos^2 x
-> (sin^2x-sin^2x*cos^2x)/cos^2x
do u understand ?

Answer 18

ok