sin2 =2tan cos
To prove the equation sin^2θ = 2tanθsinθ, we'll start by using basic trigonometric identities.
First, let's rewrite tanθ as sinθ/cosθ using the definition of tangent.
So, tanθ = sinθ/cosθ.
Now, let's rearrange the equation to isolate sinθ on one side:
tanθ = sinθ/cosθ
Multiply both sides of the equation by cosθ to eliminate the denominator:
cosθ(tanθ) = sinθ
Next, we'll use the identity sin2θ = 2sinθcosθ.
Therefore, we can rewrite the left side of the equation as sin2θ:
sin2θ = 2sinθcosθ
Now, let's substitute the value of cosθ(tanθ) we found earlier:
sin2θ = cosθ(tanθ)
Since we obtained the expression cosθ(tanθ) on both sides of the equation, we can replace it with sinθ, as we showed earlier:
sin2θ = 2tanθsinθ.
Therefore, we have proven that sin^2θ = 2tanθsinθ.