Question

4cos^3 45 - 3cos 45+ sin45

Answer 1

Step-by-step explanation:

4 cos^3 45° - 3 cos 45° + sin 45°

=> $4 (\frac{1}{\sqrt{2}})^3 - 3 (\frac{1}{\sqrt{2}}) + \frac{1}{\sqrt{2}}$

=> $4 (\frac{1}{2\sqrt{2}}) - \frac{3}{2} + \frac{1}{\sqrt{2}}$

=> $\cancel{4} (\frac{1}{\cancel{2}\sqrt{2}}) - \frac{3}{2} + \frac{1}{\sqrt{2}}$

=> $2(\frac{1}{\sqrt{2}}) - \frac{3}{2} + \frac{1}{\sqrt{2}}$

=> $\cancel{2}({\frac{1}{\cancel{\sqrt{2}}}}) - \frac{3}{2} + \frac{1}{\sqrt{2}}$

=> $\sqrt{2} - \frac{3}{2} + \frac{1}{\sqrt{2}}$

=> $\sqrt{2} - \frac{3\sqrt{2} + 2}{2\sqrt{2}}$

=> $\sqrt{2} - \frac{(\sqrt{2})(-3 + \sqrt{2})}{2\sqrt{2}}$

=> $\sqrt{2} \: \frac{-3 + \sqrt{2}}{2}$

=> $\frac{ - 3 + \sqrt{2} - 2 \sqrt{2}}{2}$

=> $\frac{(\sqrt{2})(2 - 3)}{2}$

=> $\frac{\cancel{\sqrt{2}}(2-3)}{\cancel{2}}$

=> $\large{\boxed{\pink{\frac{-1}{\sqrt{2}}}}}$