Question

Solve for xx - 15°) = 1.677" alt=" \sec(2x - 15°) = 1.677" align="absmiddle" class="latex-formula">
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Answer 1

Remember that sec=1/cos:

$\dfrac{1}{\cos(2x-15)}=1.677$

Invert both members:

$\cos(2x-15) = \dfrac{1}{1.677}$

Consider the arccos of both sides:

$\arccos(\cos(2x-15))=\arccos\left(\dfrac{1}{1.677}\right)$

Arccos and cod simplify:

$2x-15=\arccos\left(\dfrac{1}{1.677}\right)$

Add 15 to both sides:

$2x=\arccos\left(\dfrac{1}{1.677}\right)+15$

Divide both sides by 2:

$x=\dfrac{\arccos\left(\dfrac{1}{1.677}\right)+15}{2}$