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Question: The value of \(\cos(270{^\circ} + \theta)\cos(90{^\circ} - \theta) - \sin(270{^\circ} - \theta)\cos\...

The value of cos⁡(270∘+θ)cos⁡(90∘−θ)−sin⁡(270∘−θ)cos⁡θ\cos(270{^\circ} + \theta)\cos(90{^\circ} - \theta) - \sin(270{^\circ} - \theta)\cos\theta is.

A

0

B

–1

C

1/2

D

1

Answer

1

Explanation

Solution

cos⁡(270+θ)cos⁡(90−θ)−sin⁡(270−θ)cos⁡θ\cos(270 + \theta)\cos(90 - \theta) - \sin(270 - \theta)\cos\theta

=sin⁡θ.sin⁡θ+cos⁡θ.cos⁡θ=1= \sin\theta.\sin\theta + \cos\theta.\cos\theta = 1.