Question

tan(y° ) = (4cos² 9° −3)(4cos² 27° −3)

If y satisfy the equation above, find y where 0 < y < 90.
Clarification: Angles are measured in degrees.

Answer 1

Answer:

y = 9

We know

$\cos(3x) = 4 \cos {}^{3} (x) - 3 \cos(x) \\ \\ \cos(3x) = \cos(x) (4 \cos {}^{2} (x) - 3) \\ \\ for \: \cos(x) \neq0 \: \\ 4 \cos {}^{2} (x) - 3 = \frac{ \cos(3x) }{ \cos(x) }$

So now RHS is

$(4 \cos {}^{2} (9) - 3)(4 \cos {}^{2} (27) - 3) \\ \\ = \frac{ \cos(3 \times 9) }{ \cos(9) } \times \frac{ \cos(27 \times 3) }{ \cos(27) } \\ \\ = \frac{ \cos(81) }{ \cos(9) } \\ \\ = \frac{ \sin(9) }{ \cos(9) } \\ \\ = \tan(9) = tany$

So

y = 9°

Answer 2

Step-by-step explanation:

see the attachment

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