19. Prove that: 4(sin1 30°+ cos 609)-+ cos4 60°liug 5 cm From a noin

1.	19. Prove that: 4(sin1 30°+ cos 609)-+ cos4 60°liug 5 cm From a noint P 13 cm away from its centro(sin2 60cos2 45)+12cos 45°) +
Answer» 4(sin^4 30 + cos^4 60) - 2/3(sin^2 60 - cos^2 45) + 1/2 tan^2 60 = 4[(1/2)^4 + (1/2)^4] - 2/3[(sqrt(3)/2)^2 - (1/sqrt(2))^2] + 1/2[sqrt(3)^2] = 4(1/16 + 1/16) - 2/3(3/4 - 1/2) + 1/2*(3) = 8/16 - 2/3(1/4) + 3/2 = 1/2 - 1/6 + 3/2 = 2 - 1/6 = 11/6 = 1 5/6

19. Prove that: 4(sin1 30°+ cos 609)-+ cos4 60°liug 5 cm From a noint P 13 cm away from its centro(sin2 60cos2 45)+12cos 45°) +

Answer»

4(sin^4 30 + cos^4 60) - 2/3(sin^2 60 - cos^2 45) + 1/2 tan^2 60

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

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

= 8/16 - 2/3(1/4) + 3/2

= 1/2 - 1/6 + 3/2

= 2 - 1/6

= 11/6

= 1 5/6