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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

ConceptTrigonometric Ratios of an Acute Angle of a Right-angled Triangle

#### 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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#### APPEARS IN

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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