Posted by **aman** on Wednesday, June 13, 2012 at 7:08am.

if tanx+cotx=2 then the value of tan^5x + cot^10x is

- arithmetic -
**Reiny**, Wednesday, June 13, 2012 at 8:55am
If tanx + cotx = 2

sinx/cosx + cosx/sinx = 2

(sin^2 x + cos^2 x)/(sinxcosx) = 2

1/(sinxcosx) = 2

2sinxcosx= 1

sin 2x = 1

2x = 90° for 0 ≤ x ≤ 180°

x = 45° or π/4 radians

we know tan 45° = 1 and cot 45° = 1

then tan^5 x + cot^10 x

= 1^5 + 1^10

= 2

There are other solutions for x

they are x + k(180°) , where k is an integer

but all such angles will fall in either quadrant I or III and both the tangent and cotangent would be +1

so tan^5 x + cot^2 x = 2

## Answer this Question

## Related Questions

- Math - 1)A piano tuner uses a tuning fork. If middle C has a frequency of 264 ...
- Pre-Calc - How do I solve this? My work has led me to a dead end. tan(45-x) + ...
- trig - verify the identity: tan^2x(1+cot^2x)=1/1-sin^2x Verify the Id: tanx + ...
- TRIG.............. - Q.1 Prove the following identities:- (i) tan^3x/1+tan^2x + ...
- TRIGONOMETRY *(MATHS) - Q.1 Prove the following identities:- (i) tan^3x/1+tan^2x...
- pre-calc - Can someone help me find the exact value of 4csc(3pi/4)-cot(-pi/4)? ...
- Trig - Verify that each of the following is an identity. tan^2x-sin^2x=tan^2xsin...
- trigonometry - How do you find: cot(-5pie/4)? you have to know that cotx = 1/...
- Pre Cal - could someone please tell me what the other angle identity of tan is? ...
- Math-Trig - 1. Create an algebraic expression for sin(arccosx-arcsin3x) 2. The ...