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If A, B and C are interior angles of a triangle ABC, then show that sin((B+C)/2)=cos(A/2) - Mathematics

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Question

If A, B and C are interior angles of a triangle ABC, then show that `\sin( \frac{B+C}{2} )=\cos \frac{A}{2}`

Solution

∵ A + B + C = 180° (a.s.p. of ∆)

B + C = 180° – A

`( \frac{B+C}{2})=90^\circ -\frac{A}{2}`

`\sin ( \frac{B+C}{2})=\sin ( 90^\circ -\frac{A}{2})`

`\sin ( \frac{B+C}{2} )=\cos \frac{A}{2} `

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 (Latest))
Chapter 8: Introduction to Trigonometry
Ex. 8.3 | Q: 6 | Page no. 190
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 10: Trigonometric Ratios
Ex. 10.3 | Q: 6.2 | Page no. 53
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 10: Trigonometric Ratios
Ex. 10.3 | Q: 6.2 | Page no. 53
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Solution If A, B and C are interior angles of a triangle ABC, then show that sin((B+C)/2)=cos(A/2) Concept: Trigonometric Ratios of Some Specific Angles.
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