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Question
Solve for x, if:
tan (cos-1x) = `2/sqrt5`
Solution
tan (cos-1x) = `2/sqrt5`
⇒ cos-1 x = tan-1`(2/sqrt5)`
⇒ tan-1`(sqrt (1-"x"^2)/"x")` = tan-1`(2/sqrt5)`
⇒ `sqrt(1-"x"^2)/"x" = 2/sqrt5 ⇒ (1-"x"^2)/"x"^2 = 4/5`
⇒ 5 - 5x2 = 4x2 ⇒ 5 = 9x2
⇒ `5/9 = x^2 ⇒ x = ± sqrt5/3`
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