Question

prove that sinx +cos x/cosx-sinx =tan2x+sec2x

Answer 1

Hi ,

LHS = ( sin x + cos x )/( cosx - sin x )

= [(cosx+sinx)(cosx+sinx)]/[(cosx-sinx)(cosx+sinx)]

= ( cosx + sinx )²/[ cos² x - sin² x ]

= (cos²x+sin² x + 2sinxcosx)/(cos2x)

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We know that ,

1 ) cos² x - sin² x = cos 2x

2 ) cos² x + sin² x = 1

3 ) 2sinxcosx = sin2x

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= ( 1 + sin 2x )/cos 2x

= ( 1/cos 2x ) + ( sin 2x /cos 2x )

= Sec 2x + tan 2x

= RHS

I hope this helps you .

: )

Answer 2

Solution:-

sinx +cos x/cosx-sinx =tan2x+sec2x


= (sinx +cos x/cosx-sinx)×(cosx+sinx)/cosx+sinx)

=( 2sinx.cosx+ sin^2+cox^2)/[(cos^2x-sin^2x)]

= ( sin2x + 1)/cos2x

= sin2x/cos2x + 1/cos2x

= [tan2x +sec2x]proved