prove thT ( cos theta/ 1- sin theta)= sec theta + tan theta
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Cos theta/1-sin theta
Cos theta(1+sin theta)/(1+sin theta)(1-sin theta)
Cos theta ( 1+ sin theta)/cos square theta
1+sin theta/cos theta
1/cos theta +sin theta /cos theta
Sec theta + tan theta
Hence proved
Answered by
22
L.H.S=cos θ/(1-sin θ)
=[(cos θ)(1+sin θ)]/[(1-sin θ)(1+sin θ)]
=[(cos θ)(1+sin θ)]/(1-sin²θ)
=[(cos θ)(1+sin θ)]/(cos²θ)
=(1+sin θ)/cos θ
=(1/cos θ)+(sin θ/cos θ)
=sec θ+tan θ
=R.H.S
=[(cos θ)(1+sin θ)]/[(1-sin θ)(1+sin θ)]
=[(cos θ)(1+sin θ)]/(1-sin²θ)
=[(cos θ)(1+sin θ)]/(cos²θ)
=(1+sin θ)/cos θ
=(1/cos θ)+(sin θ/cos θ)
=sec θ+tan θ
=R.H.S
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