Introduction

Trigonometric Equations

• If sin θ = sin α or cosec θ = cosec α then θ = nπ + (-1)nα, n ∈ I
• If cos θ = cos α or sec θ = sec α then θ = 2nπ ± α, n ∈ I
• If tan θ = tan α or cot θ = cot α then θ = nπ + α, n ∈ I
• If sin² θ = sin² α or cos² θ = cos² α or tan²θ = tan²α then θ = nπ ± α, n ∈ I
• If cos θ = 0 then θ = nπ + π/2, n ∈ I
• If cos θ = -1 then θ = 2nπ + π, n ∈ I
• If sin θ = 0 then θ = nπ, n ∈ I
• If sin θ = 1 then θ = 2nπ + π/2, n ∈ I
• If sin θ = -1 then θ = 2nπ - π/2 n ∈ I
• Equation of the type of a cos θ + b sin θ = c

then put a = r cos α, b = r sin α so that r = √a² +b², α = tan^-1 b/a

Then the expression reduces to cos (θ - α) = c/r

Or θ - α = 2nπ ± cos^-1 (c/r)

⇒ θ = α + 2nπ ± cos^-1 (c/r), n ∈ I