Question

(sec A + tan A) (1 - sin A) = cos A​

Answer 1

Hello

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Given us,

( secA + tanA ) ( 1 - sinA )

we know that

secA = 1/cosA

tanA = sins/cosA

now

( 1 /cosA + sinA /cosA ) ( 1 - sinA )

= ( 1 + sinA ) ( 1 - sinA )/ cosA

= 1² - sin²A / cosA

= cos²A / cosA

= cosA

RHS

thanks

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Answer 2

Answer:

Taking LHS,

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

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

= [(1+sinA)/cosA](1-sinA)

= (1+sinA)(1-sinA)/cosA

= (1-sin^2 A)/cosA

= (cos^2 A)/cos A

= cos A

= RHS

HENCE PROVED ☑️☑️