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sin2x/sinx - cos2x/cosx = secx
We will start from the L.H.S and prove the identity.
We know that:
sin2x = 2sinx*cosx
cos2x = 2cos^2 x - 1
We will substitute in L.H.S.
=> 2sinxcosx/sinx - (2cos^2 x-1)/cosx
==> 2cosx - 2cos^2 x/cosx + 1/cosx
==> 2cosx - 2cosx + 1/cosx
Now we know that secx = 1/cosx
==> 1/cosx = sec x.........R.H.S
Then the identity "(sin 2x / sinx) - (cos 2x / cos x) = sec x" is TRUE.
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