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Question Number 202041 by hardmath last updated on 19/Dec/23

$$\mathrm{Simplify}:\frac{\sqrt{2}-\sin \alpha -\cos \alpha }{\sin \alpha -\cos \alpha }$$

Answered by cortano12 last updated on 19/Dec/23

$$=\frac{\sqrt{2}-\sqrt{2}(\frac{1}{\sqrt{2}}\sin \alpha +\frac{1}{\sqrt{2}}\cos \alpha )}{\sqrt{2}(\frac{1}{\sqrt{2}}\sin \alpha -\frac{1}{\sqrt{2}}\cos \alpha )}$$$$=\frac{1-\cos (\alpha -45°)}{\sin (\alpha -45°)}$$$$=\csc (\alpha -45°)-\cot (\alpha -45°)$$$$$$

Commented by hardmath last updated on 20/Dec/23

$$thankyouSer$$

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