Math, asked by bhavya2052, 11 months ago

prove that 4 cos 12 into cos 48 into cos 72 is equal to 1 minus 2 sin square 18​

Answers

Answered by devanayan2005
3

Hey mate...

4cos12°cos48°cos72°

=2(2cos12°cos48°)cos72°

=2[cos(12°+48°)+cos(12°-48°)]cos72°

=2(cos60°+cos36°)cos72°

=2cos60°cos72°+2cos36°cos72°

=2×1/2×cos72°+[cos(36°+72°)+cos(36°-72°)]

=cos72°+cos108°+cos36°

=2cos(72°+108°)/2cos(72°-108°)/2+cos36°

=2cos90°cos18°+cos36°

=cos36° (Proved)

[∵, cos90°=0]

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