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Question
If sinθ = `11/61`, find the values of cosθ using trigonometric identity.
Solution
sinθ = `11/61` ...[Given]
We have,
sin2θ + cos2θ = 1
⇒ cos2θ = 1 − sin2θ
⇒ `cos^2θ = 1 - (11/61)^2`
⇒ `cos^2θ = 1 - 121/3721`
⇒ `cos^2θ = (3721 - 121)/3721`
⇒ `cos^2θ = 3600/3721`
⇒ `cosθ = sqrt((60/61)^2)` ...[Taking square root of both sides]
⇒ cosθ = `60/61`
Thus, the value of cosθ is `60/61`.
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