Trigonometry and Modelling

a.

Show that

\cos \theta \left( 4 \tan \theta + \frac{3}{\tan \theta} \right) \equiv \sin \theta + \frac{3}{\sin \theta}

for $θ≠nπ2\theta \neq \frac{n\pi}{2}$ .

[4]

b.

Hence solve, for $2\pi$ , the equation

\cos x \left( 4 \tan x + \frac{3}{\tan x} \right) = 6 \sin x - 1

giving your answers to 3 significant figures.

[6]

a.

Show that

\cos \theta \left( 4 \tan \theta + \frac{3}{\tan \theta} \right) \equiv \sin \theta + \frac{3}{\sin \theta}

for $θ≠nπ2\theta \neq \frac{n\pi}{2}$ .

[4]

b.

Hence solve, for $2\pi$ , the equation

\cos x \left( 4 \tan x + \frac{3}{\tan x} \right) = 6 \sin x - 1

giving your answers to 3 significant figures.

[6]

Trigonometry and Modelling Questions