Question

If tanθ = 2, find the values of other trigonometric ratios.

Answer 1

tanθ = 2   ...(Given)
∴ cotθ = `1/2`
We have,

1 + tan²θ = sec²θ

1 + (2)² = sec²θ

1 + 4 = sec²θ

5 = sec²θ

Taking Square root on both sides

secθ = `sqrt5`

Cosθ = `1/secθ`

Cosθ = `1/sqrt5`

tanθ = `sinθ/cosθ`

2 = `sinθ/(1/sqrt5)`

2 = `sinθ xx sqrt5/1`

`2/sqrt5 = sinθ`

`sinθ = 2/sqrt5`
cosecθ = `1/sinθ`

= `1/(2/sqrt5)`

= `1 xx sqrt5/2`

∴ cosecθ = `sqrt5/2`