a student was asked to prove cos(x+pi)=-cosx the students work follows, where was the students mistake?

Accepted Solution

Answer:The answer is the second ⇒ cosx cosπ - sinx sinπStep-by-step explanation:∵ cos(x + π) = cosx cosπ - sinx sinπ∵ cosπ = -1∵ sinπ = 0∴ cos(x + π) = cosx(-1) - sinx(0) = -cosx - 0 = -cosxThe mistake in the rule it will not give different answer because + 0 or - 0 give us the same answer but if the measure of angle not π the answer will change.Note: cos(x + π) means the angle in the third quadrant and the value of cos in the third quadrant must be negative