Question

Cos(​π-​x)+​cos(​π/​2-​x)+​cos(​π+​x)

Answer 1

cos(π-x)+cos(π/2-x)+cos(π+x)=-сos x+cos x-cosx= -cosx

Answer 2

To simplify the expression, let's break it down step by step:

1. Start with the first term: cos(π - x). Using the identity cos(π - x) = -cos(x), we can rewrite the first term as -cos(x).

2. Move on to the second term: cos(π/2 - x). Using the identity cos(π/2 - x) = sin(x), we can rewrite the second term as sin(x).

3. Finally, let's simplify the third term: cos(π + x). Using the identity cos(π + x) = -cos(x), we can rewrite the third term as -cos(x).

Now, let's combine the simplified terms:

-cos(x) + sin(x) - cos(x)

To further simplify, let's group the like terms:

-2cos(x) + sin(x)

So, the simplified expression is -2cos(x) + sin(x).