Maharashtra State BoardHSC Science (General) 11th
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Prove the following: cosx+sinxcosx-sinx-cosx-sinxcosx+sinx = 2tan2x - Mathematics and Statistics

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Sum

Prove the following:

`(cosx + sinx)/(cosx - sinx) - (cosx - sinx)/(cosx + sinx)` = 2tan2x

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Solution

L.H.S. = `(cosx + sinx)/(cosx - sinx) - (cosx - sinx)/(cosx + sinx)`

= `((cosx + sinx)^2 - (cosx - sinx)^2)/((cosx - sinx)(cosx + sinx)`

= `((cos^2x + sin^2x + 2sinx cosx) - (cos^2x + sin^2x - 2sinx cosx))/(cos^2x - sin^2x)`

= `(1 + 2sinx cosx - 1 + 2sinx cosx)/(cos^2x - sin^2x)`

= `(2(2sinx cosx))/(cos^2x - sin^2x)`

= `(2sin2x)/(cos2x)`

= 2tan 2x

= R.H.S.

Concept: Trigonometric Functions of Double Angles
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