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Step-by-step explanation:L.H.S
1/2.cos20°[2cos80°cos40°]. , using formula 2cosA.cosB=cos(A+B)+cos(A-B).
=1/2cos20°[cos(80°+40°)+cos(80°-40°)].
=1/2cos20°[cos120° + cos40°].
=1/2.cos20°.(-1/2) + 1/2.cos40°.cos20°.
=-1/4.cos20° +1/4[2cos40°.cos20°].
=-1/4.cos20°+1/4.[cos60°+cos20°].
=-1/4.cos20°+1/4.cos60° +1/4.cos20°.
= 1/4.cos60°
= 1/4×(1/2)
= 1/8. Proved.
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