Question

Simplify $\frac{3 cos \theta + cos 3\theta}{3 sin \theta - sin 3\theta}$

Answer 1

we know,
cos3x = 4cos³x - 3cosx

sin3x = 3sinx - 4sin³x

now,
$cos3\theta=4cos^3\theta-3cos\theta\\\\sin3\theta=3sin\theta-4sin^3\theta$

$\textbf{so,}\frac{3cos\theta+cos3\theta}{3sin\theta-sin3\theta}\\\\=\frac{3cos\theta+4cos^3\theta-3cos\theta}{3sin\theta-3sin\theta+4sin^3\theta}$

= $\frac{cos^3\theta}{sin^3\theta}$

= $cot^3\theta$

Answer 2

HELLO DEAR,



we know:-
cos3θ = 4cos³θ - 3cosθ

sin3θ = 3sinθ - 4sin³θ


now, (3cosθ + cos3θ)/(3sinθ - sin3θ)

=> (3cosθ + 4cos³θ - 3cosθ)/(3sinθ - 3sinθ + 4sin³θ)

=> 4cos³θ/4sin³θ

=> cot³θ


I HOPE IT'S HELP YOU DEAR,
THANKS