Question

for theta is equal to 30 degree verify that sin 2 theta is equal to 2 Sin Theta into cos theta ​

Answer 1

sin2θ = 2 sinθ cosθ [ for θ = 30° ]

Step-by-step explanation:

Given, sin2θ = 2 sinθ cosθ

For θ = 30°,

L.H.S. = sin(2 * 30°)

= sin60°

= √3/2

& R.H.S. = 2 sin30° cos30°

= 2 * 1/2 * √3/2

= √3/2

Thus the trigonometric rule verified.

Trigonometry:

Trigonometry is the study of relations between angles and their ratios with various properties to find sine, cosine, tan, cosec, sec and cot ratios. Some properties can deduce angles in their general value apart from known definite ones. Now let us know some identities-

1. sin²θ + cos²θ = 1

2. sec²θ - tan²θ = 1

3. cosec²θ - cot²θ = 1

4. cos(A + B) = cosA cosB - sinA sinB

5. cos(A - B) = cosA cosB + sinA sinB

6. sin(A + B) = sinA cosB + cosA sinB

7. sin(A - B) = sinA cosB - cosA sinB

8. sin60° = √3 / 2

9. cos60° = 1/2

10. sin2A = 2 sinA cosA