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kogti [31]
3 years ago
5

Simplify the expression by using a double-angle formula or a half-angle formula.

Mathematics
1 answer:
Natasha2012 [34]3 years ago
5 0
Double-angle formulas:
2sinФcosФ=sin(2Ф) /:2
sinФcosФ=1/2*sin(2Ф)

sin(Ф/6)cos(Ф/6)=1/2*sin(2*Ф/6)=1/2*sin(Ф/3)

cos²Ф-sin²Ф=cos(2Ф)/*7
7cos²Ф-7sin²Ф=7cos(2Ф)

7cos²(Ф/9)-7sin²(Ф/9)=7cos(2*Ф/9)=7cos(2Ф/9)

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Use synthetic division to find the roots.  The coefficients of this cubic function are 1, -2, -5, 6, and we begin by using 1 as our first divisor:

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Because the remainder is zero (0), we can conclude that 1 is indeed a root of the given polynomial.  The quotient is 1x^2  - 1x  - 6, whose roots can be found either through synthetic division or factoring.  In this case the factors are (x - 3) and (x + 2), so the other zeros of this function are {-2, 3}.

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