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Question
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
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Solution
Given: sinθ = `11/61`
We know that,
sin2θ + cos2θ = 1
∴ `(11/61)^2 + cos^2θ` = 1
∴ `121/3721 + cos^2θ` = 1
∴ cos2θ = `1 - 121/3721`
∴ cos2θ = `(3721 - 121)/3721`
∴ cos2θ = `3600/3721`
∴ cosθ = `60/61` .......[Taking square root of both sides]
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