Question

Solve for x

`\sec(2x - 15°) = 1.677`
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Answer 1

Remember that sec=1/cos:

`(1)/(\cos(2x-15))=1.677`

Invert both members:

`\cos(2x-15) = (1)/(1.677)`

Consider the arccos of both sides:

`\arccos(\cos(2x-15))=\arccos\left((1)/(1.677)\right)`

Arccos and cod simplify:

`2x-15=\arccos\left((1)/(1.677)\right)`

Add 15 to both sides:

`2x=\arccos\left((1)/(1.677)\right)+15`

Divide both sides by 2:

`x=(\arccos\left((1)/(1.677)\right)+15)/(2)`