Math, asked by manyarao171, 10 months ago

Prove that 4.cos20.cos 40.cos 60.cos 80 =1/4

Answers

Answered by sandy1816
4

Step-by-step explanation:

4[cos20.cos40.cos60.cos80]

=4[1/2cos20(cos80.cos40)]

=4[1/4cos20(2cos80cos40)]

=4[1/4cos20{cos(80+40)+cos(80-40)]

=4[1/4cos20{cos120+cos40}]

=4[1/4cos20{cos(90+30)+cos40}]

=4[1/4cos20(-sin30+cos40)]

=4[1/4cos20(-1/2+cos40)]

=4[-1/8cos20+1/4cos20cos40]

=4[-1/8cos20+1/8(2cos20cos40]

=4[-1/8cos20+1/8{cos60+cos20}]

=4[-1/8cos20+1/8(1/2+cos20)]

=4[-1/8cos20+1/16+1/8cos20]

=4.(1/16)

=1/4

thankYou

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