If , find all the values of all the trignometeric ratios of θ.

We have, sinθ = = perpendicular/hypotenuse (For some value of k)

By Pythagoras theorem, (hypotenuse)² = (perpendicular)² + (base)²

∴AB² = BC² + AC²

{(a² + b²)k}² = {(a² - b²)k}² + AC²

a⁴k² + b⁴k² + 2a²b²k² = a⁴k² + b⁴k² - 2a²b²k² + AC²

AC² = 4a²b²k² = (2abk)²

→ AC = 2abk

Hence, the trigonometric ratios for the given θ are:

sinθ =

cosθ = AC/AB = =

tanθ = BC/AC = sinθ /cosθ =

cotθ = AC/BC = 1/tanθ =

cosecθ = AB/BC = 1/sinθ =

secθ = AB/AC = 1/cosθ =