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If A, B, C Are the Interior Angles of a δAbc, Show that Cos[(B+C)/2] = Sin A/2 - CBSE Class 10 - Mathematics

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Question

If A, B, C are the interior angles of a ΔABC, show that `cos[(B+C)/2] = sin A/2`

Solution

We have to prove: `cos[(B+C)/2] = sin A/2`

Since we know that in triangle ABC

`A + B + C = 180^@`

`=> B + C = 180^@ - A`

Dividing by 2 on both sides, we get

`=> (B +C)/2 = 90^@ - A/2`

`=> cos (B + C)/2 = cos (90^@ - A/2)`

`=> cos  (B + C)/2 = sin A/2`

Proved

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Solution If A, B, C Are the Interior Angles of a δAbc, Show that Cos[(B+C)/2] = Sin A/2 Concept: Trigonometric Ratios of an Acute Angle of a Right-angled Triangle.
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