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Question Number 129051 by oustmuchiya@gmail.com last updated on 12/Jan/21

$$provethat\frac{1+\mathit{s}\mathit{i}\mathit{n}\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}\mathit{x}\mathit{c}\mathit{o}\mathit{s}\mathit{x}}=$$$$\mathit{t}\mathit{a}\mathit{n}\mathit{x}+\mathit{c}\mathit{o}\mathit{t}\mathit{x}+\mathit{s}\mathit{e}\mathit{c}\mathit{x}\mathit{h}\mathit{e}\mathit{n}\mathit{c}\mathit{e}$$$$\mathit{d}\mathit{i}\mathit{f}\mathit{f}\mathit{e}\mathit{r}\mathit{e}\mathit{n}\mathit{t}\mathit{i}\mathit{a}\mathit{t}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{f}\mathit{u}\mathit{n}\mathit{c}\mathit{t}\mathit{i}\mathit{o}\mathit{n}$$

Answered by mindispower last updated on 12/Jan/21

$$1={cos}^2\left(x\right)+{sin}^2\left(x\right)$$$$\iff \frac{{cos}^2\left(x\right)+{sin}^2\left(x\right)+sin\left(x\right)}{cos\left(x\right)sin\left(x\right)}$$$$=\frac{cos\left(x\right)}{sin\left(x\right)}+\frac{sinx)}{cos\left(x\right)}+\frac{1}{cos\left(x\right)}$$$$=cot\left(x\right)+tan\left(x\right)+sec\left(x\right)$$

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