Question

SecA -tanA/secA+tanA = cos^2A/(1+sinA)^2

Answer 1

To Prove: (secA - tanA)/(secA + tanA) = cos²A/(1 + sinA)²

Given:

• secA = 1/cosA
• tanA = sinA/cosA

L.H.S → (secA - tanA)/(secA + tanA)

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

→ (1 - sinA)/cosA × cosA/(1 + sinA)

→ (1 - sinA)/(1 + sinA)

Multiplying by (1 + sinA)/(1 + sinA),

→ (1 - sin²A)/(1 + sinA)²

→ cos²A/(1 + sin²A) = R.H.S

Hence Proved

Answer 2

Answer:

To Prove:

(SecA - tanA) /SecA + tanA) = Cos^2A/1 + SinA)^2

Given:

• SecA = 1/CosA
• tanA = SinA/CosA

L.H.S => (SecA - tanA) / (SecA + tanA)

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

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

=> (1 - SinA) / (1 + SinA)

Multiplying by

(1 + sinA) /(1 + sinA),

=> (1 + sin^2A) / (1 + sinA) ^2

=> Cos^2A / (1 + sin^2A) = R.H.S

Step-by-step explanation:

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