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Trigonometric Ratios of Compound Angles

Solve: tan ...

Question

Solve: $tan 7 x - tan 5 x - tan 2 x = tan 7 x tan 5 x tan 2 x$ .

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Solution

We have,
$tan 7 x = tan (5 x + 2 x)$
or, $tan 7 x = \frac{tan 5 x + tan 2 x}{1 - tan 5 x . tan 2 x}$
or, $tan 7 x - tan 2 x . tan 5 x . tan 7 x = tan 5 x + tan 2 x$
or, $tan 7 x - tan 5 x - tan 2 x$ $= tan 2 x . tan 5 x . tan 7 x$

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