Math Analysis: Prove the given identity tan^2 x - sin^2 x = tan^2 x sin^2 x
ohh rewrite Tan in terms of sines and cosines and do some algebra.
thx but im still confused..
Tan = Sin/Cos Tan^2 = (Sin/Cos)^2
(Sin/Cos)^2 - Sin^2 = (Sin/Cos)^2 * Sin^2
They're asking if that's true.
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
why would you multipy sin^2 x/cos^2 x by sin^2 x?
sin^x(1-cos^2x)/cos^2x
sin^2 x/cos^2 x - sin^2 x*cos^2 x/cos^2 x -> sin^x(1-cos^2x)/cos^2x
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
So it simplifies to: Sin^2*Sin^2/Cos^2, or Sin^4/Cos^2
the answer to the equation is tan^2 x*sin^2 x
Right side: tan^2/Sin^2 = (Sin/Cos)^2/(Sin^2)
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
@iawanbahyudin where did the sin^2 x(1-cos^2 x)/cos^2 x come from?
nvm i got it thx for the help! =)
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 ?
ok
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