Question

Condense and evaluate the following expressions using identities:

cos(pi/3) * cos(5pi/6) - sin(pi/3) * sin(5pi/6)
cos(7pi/12)
(tan(122 degrees) - tan(32 degrees))/(1 + tan(122 degrees) * tan(32 degrees))
2sin(15 degrees) * cos(15 degrees)

Answer 1

To condense and evaluate the expressions, we use trigonometric identities.

Step-by-step explanation:

To condense and evaluate the given expressions, we will use various trigonometric identities.

For the first expression, we can use the identity cos(a + b) = cos(a)cos(b) - sin(a)sin(b). Plugging in the values, we get:

cos(pi/3) * cos(5pi/6) - sin(pi/3) * sin(5pi/6) = cos(pi/3 + 5pi/6)

Next, for the second expression, rearrange the terms and use the identity tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b)).

Finally, for the third expression, use the identity 2sin(a)cos(a) = sin(2a) to simplify the expression.