Question

if angle A and angle B both are obtuse angle and sin A = 12/13 , cos B = 4/5 find sin (A+B).

Answer 1

sinA=12/15
cosB=4/5=sinB=5/4=
sin(A+B)=12/13×5/4
=12×5/13×4=15/13

Answer 2

Answer:

The value of sin(A + B) is 33/65.

Step-by-step explanation:

From the above question,

They have given :

Since angle A and angle B are both obtuse, the sum of their measures must also be obtuse.

We can use the sine addition formula to find sin(A+B):

sin(A + B) = sin A cos B + cos A sin B

We know that sin A = 12/13 and cos B = 4/5, but we don't have values for cos A and sin B.

However,

       Since both A and B are obtuse, their cosines will be negative. We can use the relationship between sine and cosine to find their values:

cos A = sqrt(1 - sin$.^{2}$. A)

          = sqrt(1 - (12/13)$.^{2}$ )

          = sqrt(169 - 144)/13

          = -5/13

sin B = sqrt(1 - cos$.^{2}$  B)

         = sqrt(1 - (4/5)$.^{2}$ )

         = sqrt(1 - 16/25)

         = sqrt(9/25)

         = 3/5

Substituting these values into the sine addition formula, we get:

sin(A + B) = sin A cos B + cos A sin B

                = (12/13)(4/5) + (-5/13)(3/5)

                = (48/65) + (-15/65)

                = 33/65

So the value of sin(A + B) is 33/65.

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