Question

verify that,i 4 (sin ^4 30°+cos ^4 60°)- 3(cos 45°- sin ^2 90°)=2​

Answer 1

Correct your question first....

$\sf \boxed{To \: prove}$

$\sf </p><p>4 (sin ^4 30°+cos ^4 60°)- 3(cos^2 45°- sin ^2 90°)=2</p><p>$

$\sf \boxed{Proof}$

$\sf </p><p>=4 \{sin ^4 30°+cos ^4 (90°-30°) \} - 3(cos^2 45°- sin ^2 90°) \\\\\sf </p><p>=4 (sin ^4 30°+sin ^4 30°)- 3\{(\frac{1}{\sqrt{2}})^2 - 1\} \\\\\sf </p><p>=4(2sin^4 30°)- 3(\frac{1-2}{2}) \\\\\sf </p><p>=4(2 \: x \: \frac{1}{16})- 3(\frac{-1}{2}) \\\\\sf </p><p>= \frac{1}{2} + \frac{3}{2} \\\\\sf</p><p>=\frac{4}{2} \\\\\sf </p><p>= 2 \: \boxed{Proved} </p><p>$