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Question
Solve the following equation for x: `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
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Solution
The given equation is `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
`cos (tan^(-1) x) = sin(cot^(-1) 3/4)`
`=> cos (tan^(-1) x) = cos(pi/2 - cot^(-1) 3 /4)` `[sintheta = cos(pi/2 - theta)]`
`=> cos(tan^(-1) x) = cos(tan^(-1) (3/4))` `(tan^(-1) x + cot^(-1) x = pi/2)`
`=> tan^(-1) x = tan^(-1) (3/4)`
`=> x = 3/4`
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