prove that cos20cos40-sin5sin25=√3+1/4
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Answer:
cos 20°cos40°-L.H.S=sin5°sin25°=1/2[2cos20°cos40°-2sin25°sin5°]
=1/2[cos(40°+20°)+cos(40°-20°)-{cos(25°-5°)-cos(25°+5°)}]
=1/2[cos60°+cos20°-cos20°+cos30°]
=1/2[cos60°+cos30°]
=1/2(1/2+√3/2)
taking lcm,
=(√3+1)/4
Hence proved.
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