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# simplify the trig equation

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how to simplify tan squared X- sin squared X to tan squared X times sin squared X

Guest May 30, 2017
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#1
+80866
+2

I guess we have

[ tan^2x  -  sin^2x ] / [ tan^2x * sin^2x ]  =

[ sin^2x / cos^2x   -  sin^2x] / [ sin^2x * sin^2x / cos^2x ] =

[sin^2x  ( 1/cos^2x  - 1 ) ] / [  sin ^2x * (sin^2x / cos^2x ) ]  =

[ sec^2 x  - 1 ]  / [ sin^2x / cos^2x ]  =

tan^2x  / tan^2x   =

CPhill  May 30, 2017
#2
+5888
+1

how to simplify     tan2 x - sin2x     to     tan2x * sin2x

tan2 x - sin2x

= sin2x / cos2x    -  sin2x cos2x / cos2x

= [ sin2x - sin2x cos2x ] / cos2x

= [ sin2x ( 1 - cos2x ) ] / cos2x

= [ sin2x (sin2x) ] / cos2x

= sin2x / cos2x * sin2x

= tan2x * sin2x

hectictar  May 31, 2017

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