Question

ex 1 for theta = 30°, verify that sin 2 theta = 2 sin theta cos theta​

Answer 1

Step-by-step explanation:

given

theta=30°

apply theta =30° in the given question

that is

sin2(30°)=2sin30°.cos30°

sin60°= 2sin30°.cos30°

apply values

i.e,. √3/2=2(1/2).√3/2

√3/2= 2/2.√3/2

√3/2=1.√3/2

√3/2=√3/2

hence proved that sin2theta = 2 sin theta .cos theta.

Answer 2

Given:

• θ = 30°

To Find:

• Prove that  sin2θ = 2 sinθcosθ

Solution:

• Let LHS = 2sinθ → (1)
• Substitute the value of theta in equation (1).
• We get, LHS = sin2(30°) = sin(60°) = $\frac{\sqrt{3} }{2}$
• LHS = $\frac{\sqrt{3} }{2}$
• Consider RHS = 2sinθcosθ → (2)
• Substitute the value of theta in equation (2).
• We get, RHS = 2sin(30°)cos(30°) = 2*(1/2)*($\frac{\sqrt{3} }{2}$) = $\frac{\sqrt{3} }{2}$
• RHS = $\frac{\sqrt{3} }{2}$
• Hence, LHS = RHS

• ∴ sin2θ = 2 sinθcosθ

Hence Proved.

sin2θ = 2 sinθcosθ.