Home
Class 11
MATHS
Prove tan^(-1)(1/(p+q))+tan^(-1)(q/(p^2+...

Prove `tan^(-1)(1/(p+q))+tan^(-1)(q/(p^2+pq+1))=cot^(-1)p`

Text Solution

Verified by Experts

LHS
`tan^(-1)(1/(p+q))+tan^(-1)(q/(p^2+pq+1))`
`tan^(-1)(((1/(p+q))+(q/(p^2+pq+1)))/(1-(1/(p+q))*(q/(p^2+pq+1))))`
`tan^(-1)(((p+q)^2+1)/(p((p+q)^2+1)))`
`tan^(-1)(1/p)`
`cot^(-1)(p)`
RHS.
Promotional Banner

Similar Questions

Explore conceptually related problems

If p > q > 0a n dp r < -1 < q r , then find the value of tan^(-1)((p-q)/(1+p q))+tan^(-1)((q-r)/(1+q r))+tan^(-1)((r-p)/(1+r p)) .

If pgtqgt0 and prlt-1ltqr , then find the value of tan^(-1)((p-q)/(1+pq))+tan^(-1)((q-r)/(1+qr))+tan^(-1)((r-p)/(1+rp))

If pgtqgt0 and prlt-1ltqr , then find the value of tan^(-1)((p-q)/(1+pq))+tan^(-1)((q-r)/(1+qr))+tan^(-1)((r-p)/(1+rp))

If pgtqgt0 and prlt-1ltqr then prove that tan^(-1)((p-q)/(1+pq))+tan^(-1)((q-r)/(1+qr))+tan^(-1)((r-p)/(1+rp))=pi

If p>q>0 and pr<-1

If pgtqgt0 and prlt-1ltqr , then find the value of tan^(-1)((p-q)/(1+qr))+tan^(-1)((q-r)/(1+qr))+tan^(-1)((r-p)/(1+qr))

Prove that cot^(-1)((pq+1)/(p-q))+cot^(-1)((qr+1)/(q-r)) +cot^(-1)((rp+1)/(r-p))=0 .

tan ^ (- 1) ((1) / (p + q)) + tan ^ (- 1) ((a) / (p ^ (2) + q + 1)) = cos ^ (- 1) p

show that: cot^(-1) ((pq + 1)/(p - q)) + cot^(-1) ((qr + 1)/(q - r)) + cot^(-1)((rp + 1)/(r - p)) = 0 .

int((p+q tan^(-1)x))/(1+x^(2))dx