Question

if sin(a+b)=1/2 and cos (a+b)=1/2, then angle a=​

Answer 1

Given: sin ( A - B ) = 1/2 and cos ( A + B ) = 1/2

To find: Value of angle A?

Solution:

• Now we have given that sin ( A - B ) = 1/2 and sin takes value 1/2 when angle is 30, so sin ( A-B ) = sin 30°

              So, A-B=30°.................(i)

• Similarly,

• We have given that cos ( A + B ) = 1/2 and cos takes value 1/2 when angle is 60, so cos ( A+B ) = cos 60°

              So, A+B=60°...............(ii)

• Now, by adding (i) and (ii), we get:

              2(A) = 90°

              A= 45°

Answer:

             So, the value of angle A is 45°.

Answer 2

Step-by-step explanation:

sin (A - B) = 1/2 and cos (A + B) = 1/2

sin (A - B) = sin 30° and cos (A + B) = cos 60°

A - B = 30° and A + B = 60°

A - B = 30°

A + B = 60°

____________

2A = 90°

____________

A = 90°/2

A = 45°