Waste less time on Facebook — follow Brilliant.
Back to all chapters

Proving Trigonometric Identities

So, you've memorized your fundamental identities, but how can you prove the more obscure ones? See how to apply the basic building blocks of trig to understand deeper relationships.

Proving Trigonometric Identities: Level 4 Challenges


\[\large \tan^2 1^\circ + \tan^2 3^\circ + \tan^2 5^\circ + \cdots+ \tan^2 87^\circ + \tan^2 89^\circ = \ ? \]

\[\large \sec \left ( \dfrac {\pi}{10} \right ) \sec \left ( \dfrac {3\pi}{10} \right ) \sec \left ( \dfrac {7\pi}{10} \right ) \sec \left ( \dfrac {9\pi}{10} \right ) = \; ?\]

\[\large \dfrac1{2^x} = \cos (a) \cos(2a) \cos(3a) \cdots \cos(999a) \]

The equation above holds true for \(a = \dfrac{2\pi}{1999} \). Find \(x\).

\[\large \tan\frac{\pi}{7}\tan\frac{2\pi}{7}\tan\frac{3\pi}{7}= \sqrt{A} \] Find \(A\).

\[\large f(x) = \cos(x) \cdot \cos(2x) \cdot \cos(3x)\cdots \cos(999x)\]

If \(f \left(\dfrac{2\pi }{1999}\right) = \dfrac{1}{2^{k}}\), find \(k\).


Problem Loading...

Note Loading...

Set Loading...