Question

prove that secA + tanA - 1/tanA - secA + 1 = cosA/ ( 1-sinA)​

Answer 1

Answer:

The question is quite simple and can be proved just by changing all the Sec A and Tan A components into the terms of SinA and CosA which is exactly done in the picture attached above.

Answer 2

As we all know

sec² A - tan² A =1 and a²-b²= (a+b)(a-b)

LHS :;

=> (secA+tanA-1)/(tanA-secA+1)

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

=> {(secA+tanA)-(secA+tanA)(secA-tanA)} / (tanA-secA+1)

=> {(secA+tanA)(1-secA+tanA)/(tanA-secA+1)

=> secA+tanA = 1/cosA + sinA/cosA

=> (1+sinA)/cosA

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

= (1-sin^2 A) / cosA(1-sinA)

=> cos^2 A/cosA(1-sinA)

=> cosA/(1-sinA) = RHS

Hence proved .....

Thanku

Hope its helps you ❤️

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