The addition formulae and trigonometric identities are used to simplify or evaluate trigonometric expressions. Trigonometric equations are solved using a double angle formulae and the wave function.
Part of MathsAlgebraic and trigonometric skills
Watch this video to learn about trigonometric identities.
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There are some trigonometric identities which you must remember in order to simplify or prove trigonometric expressions when required. These are:
Show that \(\sin \left( {x - \frac{{3\pi }}{2}} \right) = \cos x\)
\(\sin \left( {x - \frac{{3\pi }}{2}} \right)\)
\(= \sin x\cos \frac{{3\pi }}{2} - \cos x\sin \frac{{3\pi }}{2}\)
\(= \sin x \times 0 - \cos x \times - 1\)
\(= \cos x\)
Show that \(\frac{{\sin (a + b)}}{{\cos a\cos b}} = \tan a + \tan b\) for \(\cos a \ne 0\) and \(\cos b \ne 0\)
\(\frac{{\sin (a + b)}}{{\cos a\cos b}} = \frac{{\sin a\cos b + \cos a\sin b}}{{\cos a\cos b}}\)
\(= \frac{{\sin a\cos b}}{{\cos a\cos b}} + \frac{{\cos a\sin b}}{{\cos a\cos b}}\)
\(= \frac{{\sin a}}{{\cos a}} + \frac{{\sin b}}{{\cos b}}\)
\(= \tan a + \tan b\)