Question

If A + B =45°, the value of
(cosAcosB – sinA sinB) is:

(a) 3 / 2
(b) 0
(c) 1/ 2
(d) None of these​

Answer 1

A + B = 45°

(cosA cosB - SinA SinB) = Cos (A + B)

Cos(A + B) = cos 45°

Cos(A + B) = $\ \frac{1}{√2}$

Option D) None of these

Answer 2

If A + B =45°, the value of ( cosA cosB – sinA sinB ) is 1/√2

Given : A + B =45°

To find :

The value of ( cosA cosB – sinA sinB )

(a) √3/2

(b) 0

(c) 1/√2

(d) None of these

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

( cosA cosB – sinA sinB )

Step 2 of 2 :

Find the value of the expression when A + B =45°

We are aware of the formula on Trigonometry that

( cosA cosB – sinA sinB ) = cos (A + B)

Thus we get

( cosA cosB – sinA sinB )

= cos (A + B)

= cos 45°

= 1/√2

Hence the correct option is (c) 1/√2

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