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Question Number 166360 by mathlove last updated on 19/Feb/22

$$\frac{\sin 10x}{sin2x}-\frac{\cos 10x}{\cos 2x}=?$$

Answered by som(math1967) last updated on 19/Feb/22

$$\frac{\mathit{s}\mathit{i}\mathit{n}10\mathit{x}\mathit{c}\mathit{o}\mathit{s}2\mathit{x}-\mathit{c}\mathit{o}\mathit{s}10\mathit{x}\mathit{s}\mathit{i}\mathit{n}2\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}2\mathit{x}\mathit{c}\mathit{o}\mathit{s}2\mathit{x}}$$$$=\frac{\mathit{s}\mathit{i}\mathit{n}(10\mathit{x}-2\mathit{x})}{\mathit{s}\mathit{i}\mathit{n}2\mathit{x}\mathit{c}\mathit{o}\mathit{s}2\mathit{x}}=\frac{2\mathit{s}\mathit{i}\mathit{n}8\mathit{x}}{2\mathit{s}\mathit{i}\mathit{n}2\mathit{x}\mathit{c}\mathit{o}\mathit{s}2\mathit{x}}$$$$=\frac{4\mathit{s}\mathit{i}\mathit{n}4\mathit{x}\mathit{c}\mathit{o}\mathit{s}4\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}4\mathit{x}}=4\mathit{c}\mathit{o}\mathit{s}4\mathit{x}$$

Commented by mathlove last updated on 19/Feb/22

$$thanks$$

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