Prove that secAtanA+cotA = sin A - Geometry Mathematics 2

प्रश्न

Prove that $\frac{\sec A}{\tan A + \cot A}$ = sin A

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उत्तर

L.H.S = $\frac{\sec A}{\tan A + \cot A}$

= $\frac{\sec A}{\frac{\sin A}{\cos A} + \frac{\cos A}{\sin A}}$

= $\frac{\sec A}{\frac{\sin^{2} A + \cos^{2} A}{\cos A \sin A}}$

= $\frac{\sec A}{\frac{1}{\cos A \sin A}}$ ......[∵ sin²A + cos²A = 1]

= sec A cos A sin A

= $\frac{1}{\cos A} \times \cos A \sin A$

= sin A

= R.H.S.

∴ $\frac{\sec A}{\tan A + \cot A}$ = sin A

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पाठ 6: Trigonometry - Q.3 (B)

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Prove that secAtanA+cotA = sin A - Geometry Mathematics 2

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Prove that secAtanA+cotA = sin A - Geometry Mathematics 2

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