Prove that Cos70° + 4 cos 70º = √3
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What is the value of cot70°+4cos70°?
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cot70°+4cos70°
=cot(90°-20°)+4 cos(90°-20°)
=tan20°+4sin20°
=sin20°/cos20°+2×2.sin20°
=(sin20°+2×2sin20°.cos20°)/cos20°
=(sin20°+2.sin40°)/cos20°
=(sin20°+sin40°+sin40°)/cos20°
=(2.sin30°.cos10°+sin40°)/cos20°
=[2×1/2.cos(90°-80°)+sin40°]/cos20°
=[sin80°+sin40°]/cos20°
=[2sin60°.cos20°]/cos20°
=[2×(1/2).(3)^1/2.cos20°]/cos20°
=(3)^1/2
√3
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