(cosec A-sin A)(sec A-cos A) =tanA+ cot A – InterviewSolution

1.

(cosec A-sin A)(sec A-cos A) =tanA+ cot A

Answer»

(cosecA-sinA)(secA-cosA)=(1/sinA-sinA)(1/cosA-cosA)

=(1-sin²A/sinA)(1-cos²A/cosA)=cos²A/sinA *sin²A/cosA=sinAcosA

LHS:1/(tanA+CotA)=1/(sinA/cosA +cosA/sinA)=1/(cos²A+Sin²A/cosAsinA)=1/1/(cosAsinA)=cosAsinA=RHS

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