Question

If cos A = `(2x)/(1 + x^2)`, then find the values of sin A and tan A in terms of x

Answer 1

cos A = `(2x)/(1 + x^2)`

In the triangle ABC

BC² = AC² – AB²

= (1 + x²)² – (2x)²

= 1 + x⁴ + 2x² – 4x²

= x⁴ – 2x² + 1

= (x² – 1)² or (1 – x²)² ...[using (a – b)²]

BC = `sqrt((x^2 - 1)^2` or `sqrt((1 - x^2)^2`

BC = x² – 1

The value of sin A = `"BC"/"AC" = (x^2 - 1)/(x^2 + 1)`

tan A = `"BC"/"AB" = (x^2 - 1)/(2x)`

and

BC = 1 – x²

The value of sin A = `(1 - x^2)/(x^2 + 1)`

tan A = `(1 - x^2)/(2x)`