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Question

The value of (secA+tanA)(1-sinA) is equal to :


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Solution

We know that secA=1cosA,tanA=sinAcosA

Now we put these values in the brackets

(secA+tanA)(1-sinA)=(1cosA+sinAcosA)(1-sinA)

(1+sinAcosA)(1-sinA1)=12-sin2AcosA((a-b)(a+b)=a2-b2)

We know that cos2A+sin2A=1,1-sin2A=cos2A

Now after putting the values the we get

1-sin2AcosA=cos2AcosA=cosA

Hence, (secA+tanA)(1-sinA)=cosA


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