Question

If `sin θ = c/sqrt(c^2 + d^2)`, where d > 0 then find the values of cos θ and tan θ.

Answer 1

In right ΔABC, ∠B = 90° and ∠BAC = θ.

Given, `sin θ = c/sqrt(c^2 + d^2) = (BC)/(AC)`.

Let BC = c and `AC = sqrt(c^2 + d^2)`.

Then, AB² = (AC² – BC²)

= (c² + d²) – c²

= d²

⇒ `AB = sqrt(d^2) = d`   ...(As d > 0).

∴ AB = d, BC = c and `AC = sqrt(c^2 + d^2)`.

∴ `cos θ = (AB)/(AC) = d/sqrt(c^2 + d^2), tan θ = (BC)/(AB) = c/d`.