Posted by NYSNC on Wednesday, December 7, 2011 at 3:59pm.
Verify the identity:
arctanx + arctan(1/x)=∏/2
using calculus theory.
(Hint: Differentiate the left hand side of the identity)

calculus  Anonymous, Wednesday, December 7, 2011 at 4:16pm
Actually, since tan(pi/2x) = cot(x)
and cot = 1/tan it falls right out.
Or, using the sum of tangents formula,
tan(arctanx + arctan(1/x))
= [tan(arctan(x)) + tan(arctan(1/x))][1  tan(arctan(x))*tan(arctan(1/x))]
= [x + 1/x]/[1  x*1/x] = (x + 1/x)/0 = oo
tan pi/2 = oo
Answer This Question
Related Questions
 Algebra2 Verify Identity  Verify the Identity: csc(x)+sec(x)/sin(x)+cos(x)=cot(...
 Calculus  Verify the identity. (Left side to right side) {(sinu+sinv)/(cosu+...
 PreCalculus  Trigonometric Functions, Radian Measure ∏ < will be ...
 trig...again  gahh i cant figure this one out either. you have you verify the ...
 Calculus  Use the integral identity: ∫(a1) (1/(1+x^2))dx=∫(11/a...
 Precalculus  Verify the identity (Left side to right side). {(cosucosv)/(cosu...
 calculus  using the intermediate value theorum, prove that arctanx = arccosx ...
 PreCalculus  A.Verify the identity. B.Determine if the identity is true for ...
 PreCalculus  A.Verify the identity. B.Determine if the identity is true for ...
 Calculus  The question is find the area of the reagion that is bounded by the ...
More Related Questions