Given that x is an acute angle and that tanx=2, without finding x find the value of: sec2x
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Luca B.
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You need to remember that `sec 2x = 1/ cos 2x` , hence, you should use the following trigonometric identity such that:
`1 + tan^2 2x = 1/(cos^2 2x)`
You need to find `tan 2x` using the following formula such that:
`tan 2x = (2 tan x)/(1 - tan^2 x)`
The problem provides the value of tan x, hence, substituting 2 for tan x yields:
`tan 2x = (2*2)/(1 - 2^2) => tan 2x = -4/3`
You need to substitute `-4/3` for `tan 2x ` in equation above such that:
`1 + (-4/3)^2 = 1/(cos^2 2x) => 1 + 16/9 =1/(cos^2 2x)`
`25/9 =1/(cos^2 2x) => 1/(cos 2x) = +-5/3`
Hence, evaluating the secant of double angle, using the provided information, yields `sec 2x = +-5/3.`
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