Question

Please solve the following sum or difference identity.

Answer 1

Answer:

$sin(A - B) = \frac{4}{5}$

Step-by-step explanation:

Given:

$sin(A) = \frac{24}{25}$

$sin(B) = -\frac{4}{5}$

Need:

$sin(A - B)$

First, let's look at the identities:

sum: $sin(A + B) = sinAcosB + cosAsinB$

difference: $sin(A - B) = sinAcosB - cosAsinB$

The question asks to find sin(A - B); therefore, we need to use the difference identity.

Based on the given information (value and quadrant), we can draw reference triangles to find the simplified values of A and B.

sin(A) = $\frac{24}{25}$

cos(A) = $\frac{7}{25}$

sin(B) = $-\frac{4}{5}$

cos(B) = $\frac{3}{5}$

Plug these values into the difference identity formula.

$sin(A - B) = sinAcosB - cosAsinB$

$sin(A - B) = (\frac{24}{25})(\frac{3}{5}) - (-\frac{4}{5})(\frac{7}{25})$

Multiply.

$sin(A - B) = (\frac{72}{125}) + (\frac{28}{125})$

Add.

$sin(A - B) = \frac{4}{5}$

This is your answer.

Hope this helps!

Answer 2

GIVEN:

sinA = 24/25

sinB = - 4/5

IDENTITIES:

• sin(A + B) = sinAcosB + cosAsinB
• sin(A - B) = sinAcosB - cosAsinB

ANSWER:

We have find the unknown trigo ratio by constructing a given right angled triangle using trigonometric function.

• cosA = 7/25 & cosB = 3/5

We know the identity of difference, so we have to just plug the respective value.

sin(A - B) = sinAcosB - cosAsinB

• (24/25 × 3/5) - (7/25 × - 4/5)
• 72/125 - (- 28/125)
• 72/125 + 28/125
• 100/125 = 4/5.

Hence, sin(A - B) = 4/5.