Today i am solving the introduction of trigonometry of exercise 8.3 and i try to solve but i did not solve the question no.6, please help me to solve this question with batter trick . If A, B and C are interior angles of a triangle ABC, then show that sin (B+C/2) = cos A/2.
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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. Q.6
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We know that, for a given triangle, sum of all the interior angles of a triangle is equal to 180°
A + B + C = 180° ….(1)
To find the value of (B+ C)/2, simplify the equation (1)
⇒ B + C = 180° – A
⇒ (B+C)/2 = (180°-A)/2
⇒ (B+C)/2 = (90°-A/2)
Now, multiply both sides by sin functions, we get
⇒ sin (B+C)/2 = sin (90°-A/2)
Since sin (90°-A/2) = cos A/2, the above equation is equal to
sin (B+C)/2 = cos A/2
Hence proved.