Question

If secθ – tanθ= a+1/a-1, then cosθ, equal to​

Answer 1

Step-by-step explanation:

Rationalise

secθ – tanθ= a+1/a-1 - equation1

(secθ - tanθ)(secθ + tanθ)/(secθ + tanθ) = a+1/a-1

(sec^2θ - tan^2θ) / (secθ + tanθ) = a+1/a-1

sec^2θ - tan^2θ

1/(secθ + tanθ) = a+1/a-1

a-1/a+1 = (secθ + tanθ) - equation 2

solve equation 1 and 2

tanθ = secθ - a+1/a-1

put this value on equation 2

secθ + tanθ = a-1/a+1

secθ = a-1/a+1 - tanθ

secθ = a-1/a+1 - secθ + a+1/a-1

2secθ = a-1/a+1 + a+1/a-1

2secθ = 2(a^2+1)/a^2-1

secθ = (a^2+1) / (a^2-1)

1/cosθ = (a^2+1) / (a^2-1)

cosθ = (a^2-1) / (a^2+1)