prove without using calculator cos2π/15.cos8π/15.cos14π/15=1/16
pls help.... show proper working
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Solution
======================
cos(2π/15) cos(4π/15) cos(8π/15) cos(14π/15)
= cos(2π/15) cos(4π/15) cos(8π/15) cos(π - π/15)
= cos(2π/15) cos(4π/15) cos(8π/15) * -cos(π/15)
= -cos(π/15) cos(2π/15) cos(4π/15) cos(8π/15)
= -16sin(π/15) cos(π/15) cos(2π/15) cos(4π/15)
cos(8π/15) / [ 16 sin(π/15) ]
= -8 * [ 2sin(π/15) cos(π/15) ] cos(2π/15)
cos(4π/15) cos(8π/15) / [ 16 sin(π/15) ]
= -8 sin(2π/15) cos(2π/15) cos(4π/15) cos(8π/15) / [ 16 sin(π/15) ]
= -4 * [ 2 sin(2π/15) cos(2π/15) ] cos(4π/15) cos(8π/15) / [ 16 sin(π/15) ]
= -4 sin(4π/15) cos(4π/15) cos(8π/15) / [ 16 sin(π/15) ]
= -2 * [2 sin(4π/15) cos(4π/15) ] cos(8π/15) / [ 16 sin(π/15) ]
= -2 sin(8π/15) cos(8π/15) / [ 16 sin(π/15) ]
= -sin(16π/15) / [ 16 sin(π/15) ]
= -sin(π + π/15) / [ 16 sin(π/15) ]
= - * -sin(π/15) / [ 16 sin(π/15) ]
= 1/16
shubhambhatt12pd0svt:
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plz help me
yes
solve the following inequalities. x^2-3x+24/x^2-4x+3 >-4...... show proper working
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