1/cos80°[(3/sin^2 40°)-(1/cos^2 40°)]
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1/cos80°[(3/sin^2 40°)-(1/cos^2 40°)]
(1/cos80°)(3/sin²40-1/cos²40)
=(1/cos80°)(√3/sin40°+1/cos40°)(√3/sin40°-1/cos40°)
=(1/cos80°)·[(√3cos40°+sin40°)/sin40°cos40°]·[(√3cos40°-sin40°)/sin40°cos40°]
=(1/cos80°)·[4sin(40°+60°)/sin80°]·[4sin(60°-40°)/sin80°]
=(1/cos80°)(4sin100°/sin80°)·(4sin20°/sin80°)
=(1/cos80°)·(4sin80°/sin80°)·(4sin20°/sin80°)
=32sin20°/sin160°
=32sin20°/sin20°
=32.
=(1/cos80°)(√3/sin40°+1/cos40°)(√3/sin40°-1/cos40°)
=(1/cos80°)·[(√3cos40°+sin40°)/sin40°cos40°]·[(√3cos40°-sin40°)/sin40°cos40°]
=(1/cos80°)·[4sin(40°+60°)/sin80°]·[4sin(60°-40°)/sin80°]
=(1/cos80°)(4sin100°/sin80°)·(4sin20°/sin80°)
=(1/cos80°)·(4sin80°/sin80°)·(4sin20°/sin80°)
=32sin20°/sin160°
=32sin20°/sin20°
=32.
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