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cos 28°cos 62°– sin 28°sin 62° = 0
From one of the trigonometric identities stated as follows;
cos(A+B) = cosAcosB - sinAsinB -----------------(i)
We can apply such identity to solve the given expression.
Given:
cos 28°cos 62°– sin 28°sin 62°
Comparing the given expression with the right hand side of equation (i), we see that;
A = 28°
B = 62°
∴ Substitute these values into equation (i) to have;
⇒ cos(28°+62°) = cos28°cos62° - sin28°sin62°
Solve the left hand side.
⇒ cos(90°) = cos28°cos62° - sin28°sin62°
⇒ 0 = cos28°cos62° - sin28°sin62° (since cos 90° = 0)
Therefore,
cos28°cos62° - sin28°sin62° = 0