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