cos45cos25 - sin 45sin25 = ??
a. cos70
b. sin70
c. cos 20
d. sin 20
which answer is correct ?
cos a cos b - sin a sin b = cos(a+b)
= cos 70
To find the value of cos45cos25 - sin45sin25, we can use the trigonometric identity, cos(a - b) = cos(a)cos(b) + sin(a)sin(b).
Let's break it down step by step:
1. Start with the given expression: cos45cos25 - sin45sin25.
2. Apply the trigonometric identity: cos(a - b) = cos(a)cos(b) + sin(a)sin(b). In this case, a = 45 and b = 25.
3. Rewrite the given expression using the identity: cos(45 - 25) = cos45cos25 + sin45sin25.
4. Simplify the expression: cos20 = cos45cos25 + sin45sin25.
So, the correct answer is option c. cos20.