Maths differentiation

1) sin 5θ = cos 4θ

sin 5θ - sin (π/2 - 4θ) = 0

2 sin (9θ/2 - π/4) cos (π/4 + θ/2) = 0

sin (9θ/2 - π/4) = 0 or cos (π/4 + θ/2) = 0

9θ/2 - π/4 = 0, π, 2π, 3π, 4π, 5π, 6π, 7π, 8π or π/4 + θ/2 = π/2

θ = π/18, 5π/18, π/2, 13π/18, 17π/18, 21π/18, 25π/18, 29π/18 or 11π/6

2) tan 4θ = cot 3θ

sin 4θ/cos 4θ = cos 3θ/sin 3θ

cos 4θ cos 3θ - sin 4θ sin 3θ = 0

cos 7θ = 0

7θ = π/2, 3π/2, 5π/2, 7π/2, 9π/2, 11π/2, 13π/2, 15π/2, 17π/2, 19π/2, 21π/2, 23π/2, 25π/2 or 27π/2

θ = π/14, 3π/14, 5π/14, π/2, 9π/14, 11π/14, 13π/14, 15π/14, 17π/14, 19π/14, 3π/2, 23π/14, 25π/14 or 27π/14

3) Pls. state the Q more clearly.

4) 2 (sin θ + cos θ) = √6

2√2 sin (θ + π/4) = √6

sin (θ + π/4) = √3/2

θ + π/4 = π/3 or 2π/3

θ = π/12 or 5π/12

2012-05-06 22:37:07 補充：
3) cosΘ-√3sinΘ=1
2[(1/2)cosΘ-(√3/2)sinΘ]=1
2[sin (π/6) cosΘ- cos (π/6) sinΘ]=1
2 sin (π/6 - Θ) = 1
sin (π/6 - Θ) = 1/2
sin (Θ - π/6) = -1/2
Θ - π/6 = - π/6 or 7π/6 or 11π/6
Θ = 0 or 4π/3 or 2π

no.3 it should be:
cosA - sqrt3 sinA = 1