Show that 1-sin 2A-cos 2A-1-sin 2A-cos 2A-tan A-

nbsp; 1+sin 2A cos 2A nbsp;/ 1+sin 2A +cos 2A nbsp; = 1+2sin A cos A 1+2sin ^ 2 A nbsp;/ 1+2sin A cos A +2cos ^ 2 A 1 nbsp;= 2sin A ...

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Trigonometric Identities

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Question

Show that $\frac{1 + sin 2 A - cos 2 A}{1 + sin 2 A + cos 2 A} = tan A$ .

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Solution

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\frac{cos 2 A}{1 - sin 2 A} = \frac{1 + tan A}{1 - tan A}

\frac{sin 2 A}{1 + cos 2 A} = tan A

\frac{cos 2 A}{1 - sin 2 A} = \frac{1 + tan A}{1 - tan A}

sin A + {sin}^{2} A = 1

{cos}^{2} A + {cos}^{4} A = 1

\frac{s i n^{2} A}{c o s^{2} A} + \frac{c o s^{2} A}{s i n^{2} A} = \frac{1}{s i n^{2} A c o s^{2} A} - 2

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