Question

simplify sin (∅+π/6) - sin(∅-π/6)​

Answer 1

Step-by-step explanation:

using expansion formulae

sin(theta + 30⁰) - sin(theta - 30⁰)

= 2cos(thetha)sin30⁰

= cos(theta)

Answer 2

Solution :-

Given that

sin (∅+π/6) - sin(∅-π/6)

We know that

π = 180°

π/6 = 180°/6 = 30°

Now,

Given expression becomes

sin(∅+30)°-sin(∅-30)°

We know that

sin (A+B) = sin A cos B + cos A sin B

sin (A-B) = sin A cos B - cos A sin B

Where, A = ∅ and B = 30°

Now,

sin(∅+30)°-sin(∅-30)°

= (sin ∅ cos 30° + cos ∅ sin 30°) -

(sin ∅ cos 30° - cos ∅ sin 30° )

= sin ∅ cos 30° + cos ∅ sin 30° -

sin ∅ cos 30° + cos ∅ sin 30°

= cos ∅ sin 30° + cos ∅ sin 30°

= 2 cos ∅ sin 30°

= 2 cos ∅ (1/2)

= (2/2) cos ∅

= (1) cos ∅

= cos ∅

Answer :-

sin (∅+π/6) - sin(∅-π/6) = cos ∅

Used formulae:-

♦ sin (A+B) = sin A cos B + cos A sin B

♦ sin (A-B) = sin A cos B - cos A sin B

♦ π = 180°

♦ sin 30° = 1/2