sin10°.cos20°.sin30°.cos40°=1/16
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Step-by-step explanation:
sin10cos20sin30cos40
=1/2 sin10(cos40cos20)
=1/4 sin10(2cos40cos20)
=1/4 sin10[cos(40+20)+cos(40-20)]
=1/4 sin10[cos60+cos20]
=1/4sin10[1/2+cos20]
=1/8sin10+1/4sin10cos20
=1/8sin10+1/8[2sin10cos20]
=1/8sin10+1/8[sin(10+20)+sin(10-20)]
=1/8sin10+1/8[sin30-sin10]
=1/8sin10+1/8[1/2-sin10]
=1/8sin10+1/16-1/8sin10
=1/16
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