Question

if sin a is 12/13 prove that sin2a=2 sin a cos a
plz its urgent​

Answer 1

Answer:

Step-by-step explanation:

sin(2a) = sin(a+a) = sinacosa+cosasina = 2sinacosa

Answer 2

EXPLANATION.

⇒ sin a = 12/13.

sin ∅ = p/h = perpendicular/hypotenuse.

⇒ sin a = 12/13 = p/h.

by using Pythagorean theorem we get,

⇒ p² + b² = h²

⇒ (12)² + (b)² = (13)².

⇒ 144 + (b)² = 169.

⇒ b² = 169 - 144.

⇒ b² = 25.

⇒ b = √25.

⇒ b = 5.

sin ∅ = perpendicular/hypotenuse = 12/13.

cos ∅ = base/hypotenuse = 5/13.

tan ∅ = perpendicular/base = 12/5.

Cosec ∅ = hypotenuse/perpendicular = 13/12.

sec ∅ = hypotenuse/base = 13/5.

cot ∅ = base/perpendicular = 5/12.

sin 2a = 2 sin(a)cos(a).

As we know that,

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

put B = A we get,

sin 2A = sin A. cos A + sin A. cos A = 2 sin A. cos A.

Similarly,

sin A = 2 sin [A/2]. cos [A/2]

sin A/2 = 2 sin [A/4]. cos [A/4].