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Question
If sec θ = `41/40`, then find values of sin θ, cot θ, cosec θ
Solution
sec θ = `41/40` ......[Given]
∴ cos θ = `1/sectheta = 1/(41/40)`
∴ cos θ = `40/41`
We know that,
sin2θ + cos2θ = 1
∴ `sin^2theta + (40/41)^2` = 1
∴ `sin^2theta + 1600/1681` = 1
∴ sin2θ = `1 - 1600/1681`
∴ sin2θ = `(1681- 1600)/1681`
∴ sin2θ = `81/1681`
∴ sin θ = `9/41` .......[Taking square root of both sides]
Now, cosec θ = `1/sintheta`
= `1/((9/41))`
= `41/9`
cot θ = `costheta/sintheta`
= `((40/41))/((9/41))`
= `40/9`
∴ sin θ = `9/41`, cot θ = `40/9`, cosec θ = `41/9`
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