Posted by aman on Wednesday, June 13, 2012 at 7:08am.
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
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 + ...
pre-calc - Can someone help me find the exact value of 4csc(3pi/4)-cot(-pi/4)? ...
TRIGONOMETRY *(MATHS) - Q.1 Prove the following identities:- (i) tan^3x/1+tan^2x...
TRIG.............. - Q.1 Prove the following identities:- (i) tan^3x/1+tan^2x + ...
Trig - Verify that each of the following is an identity. tan^2x-sin^2x=tan^2xsin...
math - solve each identity algebraically 1)(1-tanx)/(1-cotx)=-tanx 2)(1+cotx)/(1...
trigonometry - How do you find: cot(-5pie/4)? you have to know that cotx = 1/...
Trigonometry - Simply: cot(-x)-1/1-tan(-x) Is it -cotx? The other answer choice ...
For Further Reading
