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Prove that: sin theeta ( 1+ …

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Prove that: sin theeta ( 1+ tan theeta)+ cos theeta ( 1+cot theeta )= sec theeta+ cosec theeta. Pls guys. It's urgent. Answer me fast.

Posted by Archana Nair 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Bishwajeet Kumar 5 years, 1 month ago

LHS=sinA(1+tanA)+cosA(1+cotA)=sinA(1+sinA/cosA)+cosA(1+cosA/sinA) =sinA(cosA/cosA*sinA/cosA)+cosA(sinA/sinA*cosA/sinA) =(SinA*cosA+sin²A)/cosA+(sinA*cosA+cos²A)/sinA ={sinA(sinA*cosA+sin²A)+cosA(sinA*cosA+cos²A)}/cosA*sinA =[(sin2A*cosA+sin³A)+(cos²A*sinA+cos³A)]/cosA*sinA =Since sin²A=1-cos² A and cos²A=1-sin²A =[(1-cos²A)*cosA +sin³A+(1-sin²A)*sinA+cos³A]/ cosA*sinA =[cosA-cos³A+sin³A+sinA-sin³A+cos³A]/cosA*sinA =(cosA+sinA)/cosA*sinA =cosA/cosA*sinA +sinA/cosA*sinA =1/sinA+1/cosA =cosecA+secA=RHS I can't use sing of theetha in typing That's why I use 'A'.

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CBSE > Class 10 > Mathematics