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If Sin θ = 11 61 , Find the Values of Cosθ Using Trigonometric Identity. - Geometry

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If \[\sin\theta = \frac{11}{61}\], find the values of cosθ using trigonometric identity.

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Solution

We have,

\[\sin^2 \theta + \cos^2 \theta = 1\]

\[ \Rightarrow \cos^2 \theta = 1 - \sin^2 \theta\]

\[ \Rightarrow \cos^2 \theta = 1 - \left( \frac{11}{61} \right)^2 \]

\[ \Rightarrow \cos^2 \theta = 1 - \frac{121}{3721} = \frac{3721 - 121}{3721} = \frac{3600}{3721}\]

\[\Rightarrow \cos\theta = \sqrt{\left( \frac{60}{61} \right)^2} = \frac{60}{61}\]

Thus, the value of cosθ is \[\frac{60}{61}\]

Concept: Trigonometric Identities
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APPEARS IN

Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 6 Trigonometry
Problem Set 6 | Q 2 | Page 138
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