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

Prove that "tan"^(-1)(ap-q)/(aq+p)+"tan"^(-1)(b-a)/(ab+1)+"tan"^(-1)(c-b)/(bc+1)="tan"^(-1)(p)/(q)-"tan"^(-1)(1)/(c )

tan ^(-1) (cot x) + cot ^(-1) (tan x) =(pi)/(4)

Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cotA)+tan^(-1)(cot^3A) =0

Column I, Column II sin^(-1)(4/5)+2tan^(-1)(1/3)= , p. pi/6 ; sin^(-1)(12/13)+cos^(-1)(4/5)+tan^(-1)(63/16)= , q. pi/2 . If A=tan^(-1)((xsqrt(3))/(2lambda-x))a n d B=tan^(-1)((2x-lambda)/(lambdasqrt(3))) then the value of A-B is , r. pi/4 tan^(-1)1/7+2tan^(-1)1/3= , s. pi

If 0leAle(pi)/(4)," then " tan^(-1)((1)/(2)tan2A)+tan^(-1)(cotA)+tan^(-1)(cot^3A) is equal to

If pqr=1 show that (1)/(1+p+q^(-1))+(1)/(1+q+r^(-1))+(1)/(1+r+p^(-1))=1

Show that (1- tan ^(2) A ) /( cot ^(2) A-1) =tan ^(2) A

Simplify : ((p+(1)/(q))^m(p-(1)/(q))^n)/((q+(1)/(p))^m(q-(1)/(p))^n) .

If the polynomial (ax^(p)+bx^(q)-3) be divided by (x - a) and (x - b), the remainder in both the cases is (-1). Prove that (a^(p+1)-b^(q+1))/(b^(p-1)-a^(q-1))=ab