Question

4(sin^4 30deg +cos^4 60deg)-3(cos^2 45deg-sin^2 90 deg). With steps

Answer 1

Question :

$\sf \implies4( { \sin}^{4} 30 +{ \cos}^{4} 60) - 3( { \cos}^{2}45 - \sin^2 90)$

Solution :

$\sf \implies4( { \sin}^{4} 30 +{ \cos}^{4} 60) - 3( { \cos}^{2}45 -\sin^2 90) \\\\\sf \implies 4\bigg[{ \bigg( \frac{1}{2}\bigg)}^{4}+ {\bigg(\frac{1}{2}\bigg)}^{2} \:\bigg]- 3 \bigg[{ \bigg(\frac{1}{\sqrt{2}}\bigg)}^{2} - {0}^{2} \bigg] \\\\\sf \implies 4\bigg( \frac{1}{16} +\frac{1}{16}\bigg) - 3\bigg( \frac{1}{2} - 0\bigg) \\\\\sf \implies 4\bigg( \frac{1 + 1}{16}\bigg) -\frac{3}{2} \\\\\sf \implies 4\bigg( \frac{2}{16}\bigg) - \frac{3}{2} \\\\\sf \implies 4\bigg( \frac{1}{8}\bigg) - \frac{3}{2}\\ \\ \sf \implies \frac{1}{2} -\frac{3}{2} \\ \\\sf \implies \frac{1 - 3}{2} \\ \\\sf \implies \frac{ - 2}{2} \\ \\ \large\implies \boxed{ \boxed{\blue{ - 1}}}$

Answer 2

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

= 4 [(1/2)^4 + (1/2)²] -3 [(1/√2)² - 0²]

= 4(1/16 + 1/16) - 3 (1/2 - 0)

= 4(1+1/16) - 3/2

= 4(2/16) - 3/2

= 4(1/8) - 3/2

= 1/2 - 3/2

= 1-3/2

= -2/2

= -1