Simplify cos(20)cos(70)-sin(20)sin(70)

Problem

cos(20)*cos(70)−sin(20)*sin(70)

Solution

1. Identify the trigonometric identity that matches the structure of the expression. The expression follows the form cos(A)*cos(B)−sin(A)*sin(B)

2. Apply the formula for the cosine of a sum of two angles, which states cos(A+B)=cos(A)*cos(B)−sin(A)*sin(B)

3. Substitute the given values A=20 and B=70 into the identity.

cos(20+70)

4. Simplify the sum inside the parentheses.

cos(90)

5. Evaluate the cosine of 90 using the unit circle or known trigonometric values.

cos(90)=0

Final Answer

cos(20)*cos(70)−sin(20)*sin(70)=0

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