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Suppose alpha,beta,gammaa n ddelta are t...

Suppose `alpha,beta,gammaa n ddelta` are the interior angles of regular pentagon, hexagon, decagon, and dodecagon, respectively, then the value of `|cosalphasecbetacosgammacos e cdelta|` is _________

Text Solution

Verified by Experts

The correct Answer is:
1
Interior angle of regular polygon of side n is `(180^(@) - (360^(@))/(n))`
Hence, `alpha = 180^(@), beta = 120^(@), gamma = 144^(@), delta = 150^(@)`
`:. cos alpha = cos 108^(@) = - sin 180^(@) = - ((sqrt5 -1)/(4))`
`sec beta = sec 120^(@) = -2`
`cos gamma = cos 144^(@) = - cos 36^(@) = - ((sqrt5 + 1)/(4))`
`"cosec" delta = "cosec" 150^(@) = +2`
`:. |((sqrt5 -1)/(4)) (2) ((sqrt5 +1)/(4)) (-2)| = 1`
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Knowledge Check

  • If vec alpha, vec beta, vecgamma be three unit vectors such that |vec alpha+vec beta+vec gamma|=1 and vec alpha is perpendicular to vec beta while vec gamma makes angles theta and phi with vec alpha and vec beta respectively, then the value of cos theta+cos phi is -

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