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Question

1+cos 56+cos 58cos 66=

A
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C
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Solution

The correct option is C
1+cos 56+cos 58cos 66
=2 cos2 28+2 sin 62.sin 4
=2 cos2 28+2 cos 28.sin 4
=2 cos 28(cos 28+cos 86)
=2 cos 28.2 cos 57 cos 29
=4 cos 28 cos 29 sin 33.
Aliter: Apply the conditional identity
cos A+cos Bcos C=1+4 cosA2cosB2sinC2
[56+58+66=180]
We get the value of required expression equal to =4 cos 28 cos 29 sin 33.

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