Question

sin theta - sin 2 theta + sin 3 theta ÷ cos theta - cos 2 theta + cos 3 theta = cos A

Answer 1

Answer:

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Answer 2

Answer: α/2    

Given,  

sin θ + sin 2θ + sin 3θ = sin α  

(sin 3θ + sin θ) + sin 2θ = sin α  

2 sin(3θ + θ)/2 cos(3θ – θ)/2 = sin α

2 sin 2θ cos θ + sin 2θ = sin α

sin 2θ(2 cos θ + 1) = sin α….(i)

Also, given:

cos θ + cos 2θ + cos 3θ = cos α

(cos 3θ + cos θ) + cos 2θ = cos α

2 cos(3θ + θ)/2 cos(3θ – θ)/2 + cos 2θ = cos α

2 cos 2θ cos θ + cos 2θ = cos α

cos 2θ(2 cos θ + 1) = cos α….(ii)

Dividing (i) by (ii),

[sin 2θ(2 cos θ + 1)]/ [cos 2θ(2 cos θ + 1)] = sin α/cos α

tan 2θ = tan α

2θ = α

θ = α/2

Step-by-step explanation:

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