Question

1 - sin(3П/2 - a) cos (П - a)

Answer 1

Решение
1- sin(3π/2 - a)*cos(π - a) = 1 - cosa*cosa = 1 - cos²a = sin²a

Answer 2

1 - sin(3π/2 - a) + cos(π - a)

First, let's simplify the terms inside the sine and cosine functions.

3π/2 - a is equivalent to π/2 + a, because 3π/2 is equivalent to π/2 when subtracting 2π.

So, the expression becomes:

1 - sin(π/2 + a) + cos(π - a)

Now, let's evaluate the sine and cosine functions at these angles.

sin(π/2 + a) = cos(a) (using the angle addition identity for sine) cos(π - a) = -cos(a) (using the difference of angles identity for cosine)

Substitute these values back into the expression:

1 - cos(a) - cos(a)

Combine like terms:

1 - 2cos(a)

So, the final simplified expression is:

1 - 2cos(a)