Question

Prove that cos 20° cos 40° - sin 5º sin 25º = √3+1/4
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Answer 1

Answer:

Given:-

cos 20° cos 40° - sin 5º sin 25º

To Prove:

√3+1/4

​

Solution:-

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

20° cos 40° - sin 5º sin 25º = √3+1/4

​Proved.

Answer 2

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