Question

4(sin^4 30°+cos^4 60°)-3(cos^2 45°-sin^2 90°)=4.....proove it????

Answer 1

$4({ \sin}^{4} 30 + { \cos }^{4} 30) - 3( { \cos }^{2} 45 - { \sin }^{2} 90) \\ = 4( (\frac{1}{2} )^{4} + (\frac{ \sqrt{3} }{2} )^{4} ) - 3( (\frac{1}{ \sqrt{2} } )^{2} - {1}^{2} ) \\ = 4( \frac{1}{16} + \frac{9}{16} ) - 3( \frac{1}{2} - 1) \\ = 4( \frac{10}{16} ) - 3( - \frac{1}{2} ) \\ = \frac{10}{4} + \frac{3}{2} \\ = \frac{10 + 6}{4} \\ = \frac{16}{4} \\ = 4$
hope this helps..........