1.

Let alpha = (cos 85^(@) sin 55^(@)sin65^(@))/(cos5^(@)sin 35^(@)sin25^(@)) is a root of the quadratic equation 2x^(2) - px + q = 0, where p, q in Q then the value of (p + q) is

Answer»

2
5
8
10

Solution :`alpha = (cos 85^(@) sin 55^(@)sin 65^(@))/(cos 5^(@)sin 35^(@)sin 25^(@)) = (sin 5^(@)sin 55^(@)sin 65^(@))/(cos 5^(@) cos 55^(@)cos 65^(@))`
`(1/4 sin 15^(@))/(1/4 cos 15^(@)) = tan 15^(@)`
`= 2 - sqrt(3)`
other root will be `2 + sqrt(3)` [ p, q `in` Q]
So, REQUIRED equation is
`x^(2) - (4X) + 1 = 0`
2X^(2) - 8x + 2 = 0`
`:. p + q = 10`.


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