Question

If sec θ = `41/40`, then find values of sin θ, cot θ, cosec θ

Answer 1

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`