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