Question

If sin80+sin50= 2sinA.cosB then a and b is

Answer 1

Answer:

A=65,B=15

Step-by-step explanation:

formula,

sinA+sinB = 2sin(A+B/2).cos(A-B/2)

now,

A= 80+50/2

= 130/2

=65

B=80-50/2

=30/2

=15

Answer 2

Given: sin 80 + sin 50 = 2 sinA.cosB

To find: The value of A and B.

Solution:

According to one of the trigonometric equations, the following relation between sine and cosine including two variables can be written as follows.

$sin A + sin B = 2 sin \frac{A+B}{2} . cos \frac{A-B}{2}$

Now, the equation given in the question is

$sin80+sin50= 2sinA.cosB$

So, the corresponding values between the trigonometric equation and the equation in the question are equated and the values of A and B are calculated.

$A = \frac{80+50}{2}$

   $=65$

$B = \frac{80-50}{2}$

    $=15$

Therefore, the value of A and B is 65 and 15.