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/2-x) = 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+...
- Pre-Calculus - 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: ∫(a-1) (1/(1+x^2))dx=∫(1-1/a...
- Pre-calculus - Verify the identity (Left side to right side). {(cosu-cosv)/(cosu...
- calculus - using the intermediate value theorum, prove that arctanx = arccosx ...
- Calculus - The question is find the area of the reagion that is bounded by the ...
- calculus - Verify the identity: (tanx+1)/(secx+cscx) = sinx
- calculus - Verify the Identity: (Tanx + 1)/(secx + cscx) = sinx

More Related Questions