Question

If A, B and C are interior angles of a triangle ABC, then show that:

sin (

+

2

) = cos



2

.​

Answer 1

Step-by-step explanation:

Given △ABC

We know that sum of three angles of a triangle is 180

Hence ∠A + ∠B + ∠C = 180°

or A + B + C = 180°

B + C = 180° −A

Multiply both sides by 1

2

1(B + C) = 90°- A.....(1)

2 2

Now

1(B+C)

2

Taking sine of this angle

sin(B+C) (B+C=90°-A)

2 2 2

sin(90°-A)

2

cos A [sin(90°-0=cos 0]

2

Hence sin(B+C)=cos A proved

2 2