Question

If secɵ - tanɵ = √2 tanɵ, then show that secɵ + tanɵ = √2 secɵ. Kindly answer quickly! ​

Answer 1

Step-by-step explanation:

We have given;

secɵ - tanɵ = √2tanɵ;

We need to show : secɵ + tanɵ = √2 secɵ. (i)

Using given equation, we can write;

(secθ - tanθ) / tanθ = √2;

(secθ / tanθ) - 1 = √2;

secθ / tanθ = √2 + 1;

tanθ = secθ / (√2 + 1) ; (ii)

Put the value of eq. (ii) in eq. (i);

secθ + secθ/(√2 + 1) = √2 secɵ;

{(√2 + 1)secθ + secθ } / (√2 + 1) = √2 secθ

secθ {(√2 + 1 + 1)} = √2 secɵ * (√2 + 1)

√2 + 2 = √2(√2 + 1);

√2 + 2 = 2 + √2

2 + √2 = 2 + √2

Hence, LHS = RHS.

That's all.