Math, asked by sudhirmalikk, 1 year ago

prove that secA+tanA-1/tanA-secA+1 =cosA/1-sinA

Answers

Answered by veena64
9
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Answered by JackelineCasarez
1

sec A + tanA - 1/tanA - secA +1 = cosA/1-sinA

Step-by-step explanation:

As we know,

sec^2 - tan^2= 1

= (secA+tanA-(sec^2 A - tan ^2A)) /tanA-secA+1)

We know also that,

a^2-b^2 = (a+b)(a-b)

By putting this,

= (sec A + tan A - (sec A + tan A) ( sec A - tan A) / ( tanA - secA+1)

= ( sec A + tan A ) ( 1- (sec A - tan A)/ ( tanA - secA+1)

= (sec A + tan A)/(+ tan A - sec A)/(tan A - sec A+ 1)

= (sec A + tan A)

We get,

= 1/cos A + sin A/cos A

= (1+ sin A) / cos A

= (1 + sin A )(1- sin A)/(cos A (1- sin A))

= (1- sin ^2 A/(cos A (1- sin A))

= cos ^2 A / (cos A (1- sin A))

= cos A /(1- sin A)

∵ proved.

Learn more: Sec A + tan A

brainly.in/question/19568554

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