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Question
For triangle ABC, show that:
`sin (("A + B")/(2)) = cos "C"/(2)`
Sum
Solution
We know that for a triangle ΔABC
A + B + C = 180°
A + B = 180° - C
L.H.S. = sin `("A"+"B")/2`
= sin `(180- "C")/2`
= sin `(180/2-"C"/2)`
= sin `(90-"C"/2)`
= cos `("C"/2)`
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Complementary Angles for Sine ( Sin ) and Cosine ( Cos )
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