Precalculus: Establish the identity. sin(2theta) tan theta+ cos(2 theta) = 1

Question

Establish the identity.

sin(2theta) tan theta+ cos(2 theta) = 1

Answer 1

Hi Katelyn A.,

sin(2θ)tan(θ) + cos(2θ) = 1

2sin(θ)cos(θ)tan(θ) + cos²(θ) - sin²(θ) = 1

2sin(θ)cos(θ)sin(θ)/cos(θ) + cos²(θ) - sin²(θ) = 1

2sin²(θ) + cos²(θ) - sin²(θ) = 1

2sin²(θ) - sin²(θ) + cos²(θ) = 1

sin²(θ) + cos²(θ) = 1

I hope this helps, Joe.

Answer 2

(sin2θtanθ + cos2θ = 1; sin2θsinθ + cos2θcosθ)/cosθ = cos(2θ - θ)/cosθ = cosθ/cosθ = 1