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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.
\[\large \tan^2 1^\circ + \tan^2 3^\circ + \tan^2 5^\circ + \cdots+ \tan^2 87^\circ + \tan^2 89^\circ = \ ? \]
by
Thiago Bersch
\[\large \sec \left ( \dfrac {\pi}{10} \right ) \sec \left ( \dfrac {3\pi}{10} \right ) \sec \left ( \dfrac {7\pi}{10} \right ) \sec \left ( \dfrac {9\pi}{10} \right ) = \; ?\]
by
Sharky Kesa
\[\large \dfrac1{2^x} = \cos (a) \cos(2a) \cos(3a) \cdots \cos(999a) \]
The equation above holds true for \(a = \dfrac{2\pi}{1999} \). Find \(x\).
by
Dhanvanth Balakrishnan
\[\large \tan\frac{\pi}{7}\tan\frac{2\pi}{7}\tan\frac{3\pi}{7}= \sqrt{A} \] Find \(A\).
by
Mateus Gomes
\[\large f(x) = \cos(x) \cdot \cos(2x) \cdot \cos(3x)\cdots \cos(999x)\]
If \(f \left(\dfrac{2\pi }{1999}\right) = \dfrac{1}{2^{k}}\), find \(k\).
by
Aaron Jerry Ninan