Question

prove the the identity (secA+tanA) (1-sinA)=cosA​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

LHS = ( secA + tanA )(1-sinA)

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

taking LCM

= { (1+sinA) ÷ cosA } (1-sinA)

= (1+ sinA)(1 - sinA) ÷ cosA

{ (a²-b²) = (a+b)(a-b) }

= ( 1² - sin²A ) ÷ cosA

= cos²A ÷ cosA

= cosA = RHS

LHS = RHS

hence proved