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Question

Mathematics Question on Trigonometric Functions

Find the value of sin(40+θ)cos(10+θ)cos(40+θ)sin(10+θ)sin(40^{\circ} + \theta) cos(10^{\circ} + \theta) - cos(40^{\circ} + \theta) sin(10^{\circ} + \theta).

A

1/21/2

B

1/41/4

C

11

D

00

Answer

1/21/2

Explanation

Solution

We have, sin(40+θ)cos(10+θ)cos(40+θ)sin(10+θ)sin\left(40^{\circ}+ \theta\right)\cdot cos\left(10^{\circ} + \theta\right) - cos\left(40^{\circ} + \theta\right)\cdot sin\left(10^{\circ} + \theta\right) =sin\left\\{\left(40^{\circ}+\theta\right)-\left(10^{\circ}+\theta\right)\right\\} =sin30=12=sin30^{\circ}=\frac{1}{2}