Solve the equation `cos(tan^(-1)x) = sin(cot^(-1)'3/4)`.

Answer

N/a

Explanation

We have, `cos(tan^(-1)x)=sin(cot^(-1)'3/4)`
`rArr cos(cos^(-1)'(1)/(sqrt(x^(2)+1)))=sin(sin^(-1)'4/5)`
Let `tan^(-1)x = theta_(1) , rArr tantheta_(1) = x/1`
`rArr costheta_(1) = 1/(sqrt(x^(2)+1)) rArrtheta_(1) = cos^(-1)'(1)/(sqrt(x^(2)+1))`
and `cot^(-1)'3/4 = theta_(2) rArr cottheta_(2) = 3/4`
`rArr sintheta_(2) = 4/5 rArr theta_(2) = sin^(-1)'4/5`

`rArr (1)/(sqrt(x^(2)+1)) = 4/5`
{ `:' cos (cos^(-1)x)=x,x in [-1,1]` and `sin(sin^(-1)x)=x,x in[-1,10`}
On squaring both sides, we get
`16(x^(2)+1) = 25`
`rArr 16x^(2)=9`
`rArr x^(2) = (3/4)^(2)`
`:. x = +- 3/4 = (-3)/(4),3/4`