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Question Number 129594 by bagjagunawan last updated on 16/Jan/21

Commented by bemath last updated on 17/Jan/21

$$\sin \mathrm{x}+\cos \mathrm{x}+\frac{1+\sin \mathrm{x}+\cos \mathrm{x}}{\cos \mathrm{x}\sin \mathrm{x}}=$$$$\sin \mathrm{x}+\cos \mathrm{x}+\frac{2\cos \left(\frac{\mathrm{x}}{2}\right)(\sin \left(\frac{\mathrm{x}}{2}\right)+\cos \left(\frac{\mathrm{x}}{2}\right))}{2\sin \left(\frac{\mathrm{x}}{2}\right)\cos \left(\frac{\mathrm{x}}{2}\right)\cos \mathrm{x}}=$$$$\sin \mathrm{x}+\cos \mathrm{x}+\frac{1}{\sin \left(\frac{\mathrm{x}}{2}\right)(\cos \left(\frac{\mathrm{x}}{2}\right)-\sin \left(\frac{\mathrm{x}}{2}\right))}=$$$$\sin \mathrm{x}+\cos \mathrm{x}+\frac{2}{\sin \mathrm{x}-1+\cos \mathrm{x}}=$$$$\sin \mathrm{x}+\cos \mathrm{x}+\frac{2}{\sin \mathrm{x}+\cos \mathrm{x}-1}=\frac{{(\sin \mathrm{x}+\cos \mathrm{x})}^2-(\sin \mathrm{x}+\cos \mathrm{x})+2}{\sin \mathrm{x}+\cos \mathrm{x}-1}=$$$$$$

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