Question

If sin405=1/√2 then prove that sin375=√3-1/2√2

Answer 1

     

$\sin^2405+\cos^2405=1 \\ \\ \Rightarrow\ (\frac{1}{\sqrt{2}})^2+\cos^2405=1 \\ \\ \Rightarrow\ \frac{1}{2}+\cos^2405=1 \\ \\ \Rightarrow\ \cos^2405=1-\frac{1}{2} \\ \\ \Rightarrow\ \cos^2405=\frac{1}{2} \\ \\ \Rightarrow\ \cos 405=\sqrt{\frac{1}{2}} \\ \\ \Rightarrow\ \cos 405=\frac{1}{\sqrt{2}}$

$\sin 375 \\ \\ \Rightarrow\ \sin (405-30) \\ \\ \Rightarrow\ \sin 405 \cdot \cos 30 - \cos 405 \cdot \sin 30 \\ \\ \Rightarrow\ \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{3}}{2}-\frac{1}{\sqrt{2}}\cdot\frac{1}{2} \\ \\ \Rightarrow\ \frac{1}{\sqrt{2}}(\frac{\sqrt{3}}{2}-\frac{1}{2}) \\ \\ \Rightarrow\ \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{3}-1}{2} \\ \\ \Rightarrow\ \frac{\sqrt{3}-1}{2\sqrt{2}}$

$\sf{Hence proved! \\ \\ \\ Plz mark it as the brainliest. \\ \\ \\ Thank you. :-)}$

     

Answer 2

Answer:

See the attachment

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