Maharashtra State Board course SSC (English Medium) Class 10th Board Exam
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If Tanθ = 1 Them, Find the Values of Sin θ + Cos θ Sec θ + C O S E C θ - Geometry

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Question

If tanθ = 1 them, find the values of

\[\frac{\sin\theta + \cos\theta}{\sec\theta + cosec\theta}\]

Solution

tanθ = 1
We know that, tan45º = 1
∴ θ = 45º
Now,
\[\sin45^\circ = \frac{1}{\sqrt{2}}\]
\[\cos45^\circ = \frac{1}{\sqrt{2}}\]
\[\sec45^\circ = \sqrt{2}\]
\[cosec45^\circ = \sqrt{2}\]
\[\therefore \frac{\sin\theta + \cos\theta}{\sec\theta + cosec\theta} = \frac{\sin45^\circ + \cos45^\circ}{\sec45^\circ + cosec45^\circ} = \frac{\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}}{\sqrt{2} + \sqrt{2}} = \frac{\frac{2}{\sqrt{2}}}{2\sqrt{2}} = \frac{1}{2}\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 6: Trigonometry
Practice set 6.1 | Q: 5 | Page no. 131
Solution If Tanθ = 1 Them, Find the Values of Sin θ + Cos θ Sec θ + C O S E C θ Concept: Application of Trigonometry.
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