Question

Prove that 1 + sec – tan /1 + sec + tan= 1 –sin/cos θ

Answer 1

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Answer 2

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Sol:-L.H.S = 1 + secA – tanA / 1 + secA + tanA , R.H.S =1 – sinA / cosA

= L.H.S(sec2A – tan2A) + secA – tanA / 1 + secA + tanA

As we know that [sec2A – tan2A = 1]

Here, L. H. S= (secA – tanA) (secA + tanA) + (secA – tanA) / 1 + secA + tanA

L.H.S = (secA – tanA) (1+secA + tanA) / 1 + secA + tanA

L.H.S = secA – tanA

We know about the formula of secA and tanA,[secA = 1 / cosA], [ tanA = sinA / cosA]

putting the value of secA and tanA

so = 1 / cosA - sinA / cosA

L.H. S= 1 – sinA / cosA

So here L.H. S is equal to R.H.S....Proved

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