What is cos(pi+x)+cos(x-pi) ?

The solution to cos(pi+x)+cos(x-pi) is -2cos(x)

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simplify cos(pi+x)+cos(x-pi)

simplify

cos (π + x) + cos (x - π)

- 2 cos (x)

Solution steps

cos (π + x) + cos (x - π)

Rewrite using trig identities

= cos (π + x) - cos (x)

Rewrite using trig identities

= - cos (x) - cos (x)

Add similar elements:

- cos (x) - cos (x) = - 2 cos (x)

= - 2 cos (x)

cos (2 x + \frac{π}{2})

sin (27 0^{\circ} - x)

cos (arctan (\frac{x}{5}))

csc (arccot (x))

cos (- πn)