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CosA-sinA+1/cosA+sinA-1=cosecA+cotA

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CosA-sinA+1/cosA+sinA-1=cosecA+cotA

Posted by Aqsha Aqsha 8 years, 4 months ago

CBSE > Class 10 > Mathematics

4 answers

Aqsha Aqsha 8 years, 2 months ago

Thank you so much.

Rashmi Bajpayee 8 years, 4 months ago

{tex}{{\cos {\rm{A}} - \sin {\rm{A}} + 1} \over {\cos {\rm{A}} + \sin {\rm{A}} - 1}}{/tex}

Dividing all terms by sin A, we get

{tex}{{\cot {\rm{A}} - 1 + \cos ec{\rm{A}}} \over {\cot {\rm{A}} + 1 - \cos ec{\rm{A}}}}{/tex}

= {tex}{{\cot {\rm{A}} + \cos ec{\rm{A}} - 1} \over {\cot {\rm{A}} - \cos ec{\rm{A}} + 1}}{/tex}

= {tex}{{\cot {\rm{A}} + \cos ec{\rm{A}} - \left( {\cos e{c^2}{\rm{A}} - {{\cot }^2}{\rm{A}}} \right)} \over {\cot {\rm{A}} - \cos ec{\rm{A}} + 1}}{/tex}

= {tex}{{\cot {\rm{A}} + \cos ec{\rm{A}}\left( {1 - \cos ec{\rm{A}} + \cot {\rm{A}}} \right)} \over {\cot {\rm{A}} - \cos ec{\rm{A}} + 1}}{/tex}

= {tex}{\cot {\rm{A}} + \cos ec{\rm{A}}}{/tex}

Hence proved

Prity Kumari 8 years, 4 months ago

cosA-sinA+1/cosA+sinA-1= 1/sinA+cosA/sinA cosA-sinA+1/cosA+sinA-1=sinA+cosAsinA/sin (square)A cosA-sinA+1/cosA+sinA-1=sina(1+cosA)/sin(square)A cosA-sinA+1/cosA+sinA-1=1+cosA/sinA sinAcosA-sin(square)A+sinA=cosA+sinA-1+cos(square)A+sinAcosA-cosA(by cross multiplication) sincosA-sin(square)A+sinA=cosA+sinA-1+1-sin(square)A+sinAcosA-cosA 0=0 Hence proved

Devraj Singh 8 years, 4 months ago

Yes

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