Question

If sinA=4/5 and sinB=3/7 .
Find sin(A+B)

Answer 1

Answer:

answer is 7/12

Step-by-step explanation:

4/5+3/7

7/12

This only the answer for sin(A+B)

Answer 2

Given,

sinA=4/5 and sinB=3/7

To Find,

sin(A+B)

Solution,

sin(A+B) = sinAcosB + sinBcosA

$\sin {}^{2} (x) + \cos {}^{2} (x) = 1$

cosA =

$\sqrt{1 - \sin { {}^{2} }(a) }$

cosA =

$\frac{3}{5}$

cosB =

$\sqrt{1 - \sin {}^{2} (b {}^{} ) }$

cosB =

$\frac{ \sqrt{40} }{7}$

Therefore, Sin(A+B) =

$(\frac{4}{5} \times \frac{ \sqrt{40} }{7} \: )+ (\frac{3}{7} \times \frac{3}{5} )$

Hence, sin(A+B) =

$\frac{8 \sqrt{10} + 9 }{35}$

So the final answer comes out be

$\frac{8 \sqrt{10} + 9 }{35}$