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Question Number 128643 by liberty last updated on 09/Jan/21

$$\mathrm{If}\tan \mathrm{x}+\sec \mathrm{x}=\mathrm{b}\mathrm{then}\cos \mathrm{x}=?$$

Commented by john_santu last updated on 09/Jan/21

$$\tan \mathrm{x}=\mathrm{b}-\sec \mathrm{x}$$$$\mathrm{squaring}\Rightarrow \tan {}^2\mathrm{x}={\mathrm{b}}^2-2\mathrm{bsec}\mathrm{x}+\sec {}^2\mathrm{x}$$$$\Rightarrow \sec {}^2\mathrm{x}-1={\mathrm{b}}^2-2\mathrm{bsec}\mathrm{x}+\sec {}^2\mathrm{x}$$$$\Rightarrow 2\mathrm{bsec}\mathrm{x}={\mathrm{b}}^2+1\Rightarrow \cos \mathrm{x}=\frac{2\mathrm{b}}{{\mathrm{b}}^2+1}.$$

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