Question

Find the exact value of$\sin 40°-\cos 50°$.

Short answer

The value of the given expression is 0.

Step-by-step solution

Step 1. Given Information

The given expression is$\sin 40°-\cos 50°$.

Step 2. Simplify

• Rewrite $40°$as $90°-50°$in the given expression.

role="math" localid="1646826365197" $\sin 40°-\cos 50°=\sin (90°-50°)-\cos 50°$

• The angle $(90°-50°)$lies in the first quadrant and sine angle is positive is first quadrant. So, $\sin (90°-50°)=\cos 50°$.
• Substitute into the obtained equation.

$\cos 50°-\cos 50°=0$