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

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

Posted by Aqsha Aqsha 7 years, 9 months ago

CBSE > Class 10 > Mathematics

4 answers

Aqsha Aqsha 7 years, 7 months ago

Thank you so much.

0Thank You

Rashmi Bajpayee 7 years, 9 months ago

${{\cos {\rm{A}} - \sin {\rm{A}} + 1} \over {\cos {\rm{A}} + \sin {\rm{A}} - 1}}$

Dividing all terms by sin A, we get

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

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

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

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

= ${\cot {\rm{A}} + \cos ec{\rm{A}}}$

Hence proved

1Thank You

Prity Kumari 7 years, 9 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

0Thank You

Devraj Singh 7 years, 9 months ago

Yes

1Thank You

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