Question

Evaluate 2(cos4 60 - sin4 30) -(tan2 60+ cos2 45)+ 3 sec2 30

Answer 1

we know that cos(90-A) =sinA
=2(cos^4(90°-30°) - sin^4 30°)-(√3×√3 +1/√2 ×1/√2)+3 × 2/√3 ×2/√3
=2(sin^4 30° - sin^4 30°)-(√3×√3 +1/√2 ×1/√2) + 3 × 2/√3 ×2/√3
=2×0 - (3+1/2) + 4
=4-7/2
=1/2 or 0.5
by using tan60°=√3
cos45°=1/√2
sec30°=2/√3