Prove that `cot(pi/4-2cot^(- 1)3)=7`

Answer

N/a

Explanation

We have to prove. `cot(pi/4-2cot^(-1)3) = 7`
`rArr (pi/4-2cot^(-1)3)=cot^(-1)7`
`rArr (2cot^(-1)3) = (pi)/(4) - cot^(-)7`
`rArr (2cot^(-1)3) = pi/4 - cot^(-1)7`
`rArr 2tan^(-1)'(1)/(3)= (pi)/(4) - tan^(-1)'(1)/(7)`
`rArr 2 tan^(-1)'1/3+tan^(-1)'1/7 = (pi)/(4)`
`rArr tan^(-1)'(2//3)/(1-(1//3)^(2)) + tan^(-1)'(1)/(7) = (pi)/(4)`
`rArr tan^(-1)'(2//3)/(8//9) + tan^(-1)'1/7 = (pi)/(4)`
`rArr tan^(-1)'(3)/(4) + tan^(-1)'1/7 = (pi)/(4)`
`rArr tan^(-1)'((3)/(4) + (1)/(7))/(1-(3)/(7).(1)/(7))=(pi)/(4)`
`rArr tan^(-1)'((21+4)//28)/((28-3)//28)=(pi)/(4)`
`rArr tan^(-1)'(25)/(25) = (pi)/(4)`
`rArr 1 = tan '(pi)/(4)`
`rArr 1 = 1`
`rArr LHS = RHS`