Question

cos(45-A) cos(45+B) -sin (45-A)sin(45+B)
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Answer 1

Hope u like the answer .

Answer 2

Answer:

Question:-

• Evaluate: cos(45° - A) cos(45° - B) - sin(45° - A) sin(45° - B)

Answer

Identity used :

• cos(A + B) = cosA cosB - sinA sinB
• cos[90° - (A + B)] = sin(A + B)

Solution:-

cos(45° - A) cos(45° - B) - sin(45° - A) sin(45° - B)

Let 45° - A = x and 45° - B = y

So above can be rewritten as

$\bf\implies \:cosx \: cosy - sinx \: siny$

$\bf\implies \:cos(x + y)$

Put values of x and y, we get

$\bf\implies \:cos(45° - A + 45° - B)$

$\bf\implies \:cos(90° - (A + B))$

$\bf\implies \:sin(A + B)$

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