Question

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

Name: Problem 6, Chapter 8: NCERT Class 10 - Math
Uploaded: 2021-06-26T02:42:11-08:00
Duration: 3 min 43 s
Channel: Anas Venkitta
Description: If A. B and C are interior angles of a triangle ABC, then show that sin((B+C)/(2))=cos(A)/(2)

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

NCERT Class 10 - Math

Parvin Sinclair,… 1st Edition

Chapter 8, Problem 6

Instant Answer

Solved by Expert Anas Venkitta

06/26/2021

Step 1

So, we have: \[A + B + C = 180°\] Show more…

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

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Key Concepts

Co-function Identity

The co-function identity states that the sine of an angle is equal to the cosine of its complement, specifically sin(?/2 ? x) = cos x. This identity is crucial when converting between sine and cosine expressions, particularly in proofs where angles are expressed as halves or complements of other angles.

Triangle Angle Sum Theorem

In any triangle, the sum of its interior angles is always ? radians (or 180°). This theorem is key to expressing one angle in terms of the other two, which is essential when establishing relationships between trigonometric expressions of different angles within a triangle.

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