Question

cos 20° cos 40° - sin 5° sin 25°=√3+1÷4

Answer 1

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
............................................. proved.....................................
please mark me brainliest

Answer 2

Answer:√3+1/4

Step-by-step explanation:

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)

=(√3+1)/4

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