Prove that 4.cos20.cos 40.cos 60.cos 80 =1/4
Answers
Answered by
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
Similar questions