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Question
Solve the following equation `cos(tan^-1x) = sin(cot^-1 3/4)`
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Solution
Given that `cos(tan^-1x) = sin(cot^-1 3/4)`
⇒ `cos[cos^-1 1/sqrt(1 + x^2)] = sin[sin^-1 4/5]` ......
⇒ `1/sqrt(1 + x^2) = 4/5`
Squaring both sides we get,
`1/(1 + x^2) = 16/25`
⇒ `1 + x^2 = 25/16`
⇒ `x^2 = 25/16 - 1 = 9/16`
⇒ x = `+- 3/4`
Hence, x = `(-3)/4, 3/4`.
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