Question

Evaluate:
4(sin^4 30°+cos^4 60°)-3(cos^45°-sin^2 90°)+5sec^2 30°)​

Answer 1

Explanation:

4(sin^4 30°+cos^4 60°)-3(cos^2 45°-sin^2 90°)+5(sec^2 30°)

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sin 30°=1/2

cos 60°=1/2

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cos 45°=1/√2

sin 90°=1

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sec 30°=2/√3

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

+5[(2/√3)^2]

•4[(1/16) + (1/16)]-3[(1/4)-(1)]+5[(4/3)]

•4(1+1/16)-3(1-4/4)+20/3

•4(2/16)-3(-3/4)+20/3

•4(1/8)+9/4+20/3

•(4/8)+(9/4)+(20/3)

•(1/2)+(9/4)+(20/3)

•(6+27+80/12)....... {LCM}

•(113/12)

Simplified form~ 9.4