Question

If \[ \tan(60^\circ+\theta)\tan(60^\circ-\theta) = \frac{a\cos^2\theta-b}{a\cos^2\theta-c}, \] then \[ \frac{a+c}{b}= \]

• A. \(3\)
• B. \(5\)
• C. \(7\)
• D. \(9\)

Hint:

Use the tangent addition formula first, then convert everything into \(\cos^2\theta\) using \[ \boxed{\tan^2\theta=\dfrac{1-\cos^2\theta}{\cos^2\theta}}. \] Finally compare the numerator and denominator with the given expression.

Answer 1

The Correct Option is C