Question

asked Sep 2, 2023 30.8k views

1 Answer

E J Chathuranga · Answer 1 · 2023-09-09T07:30:44+0000

Explanation:

$\tan(2x) = 1.5$

Take the arc tangent,

$\tan {}^( - 1) ( \tan(2x) ) = \tan {}^( - 1) (1.5)$

2x = 56.3

x = 28.15

b.

$(3 \cos(x) + 1)(2 \cos(x) + 3) = - 2$

$6 \cos {}^(2) (x) + 11 \cos(x) + 3 = - 2$

$6 \cos {}^(2) (x) + 11 \cos(x) + 5 = 0$

$6 \cos {}^(2) (x) + 6 \cos(x) + 5 \cos(x) + 5 = 0$

$6 \cos(x) ( \cos(x) + 1) + 5( \cos(x) + 1) = 0$

$(6 \cos(x) + 5)( \cos(x) + 1) = 0$

Set each factor equal to zero.

$6 \cos(x) + 5 = 0$

$6 \cos(x) = - 5$

$\cos(x) = - (5)/(6)$

$x = \cos {}^( - 1) ( (5)/(6) )$

x = 146.4

For the second factor,

$\cos(x) + 1 = 0$

$\cos(x) = - 1$

x = 180

So the answer for the second one is

146.4 and 180.

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