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

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

= (tanA + secA + tan2A - sec2A) /( tanA - secA + 1)

as sec2A - tan2A =1

= [tanA + secA +(tanA + secA)(tanA - secA)]/ tanA - secA + 1

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

=tanA + secA

= sinA / cosA + 1/cosA

= sinA + 1 / cosA

=RHS

  • 51

Here is the link for the answer to your query:

http:// www.meritnation.com/ discuss/ question/ 2971262/ 1/

Consider the solution till 3rd last step only for your question.

  • 4

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

LHS = tanA + secA -1 / tanA - secA + 1

= tanA + secA + tan2A - sec2A / tanA - secA + 1

as tan2A + 1 = sec2A

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

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

=tanA + secA

= sinA / cosA + 1/cosA

= sinA + 1 / cosA

I hope it help u

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