Question

Solve the following equations:

(i) sin θ + cos θ = √2

(ii) sin θ + √3 cos θ = 1 

(iii) cot θ + cosec θ = √3

(iv) tan θ + tan(θ + π/3) + tan(θ + 2π/3) = √3

(v) cos 2θ = (√5 + 1)/4

(vi) 2 cos² x - 7 cos x + 3 = 0

Answer 1

(i) sin θ + cos θ = √2

Multiplying by 1/√2 on both sides

(ii) sin θ + √3 cos θ = 1 

Multiplying by 1/√(1 + 3) = 1/2 we get

(iii) cot θ + cosec θ = √3

The general soln is θ

(iv) tan θ + tan(θ + π/3) + tan(θ + 2π/3) = √3

Now

(v) cos 2θ = (√5 + 1)/4

(vi) 2 cos² x - 7 cos x + 3 = 0