If tanθ + cotθ = 5, then

If tanθ + cotθ = 5, then tan2θ + cot2θ is:

  1. 25
  2. 26
  3. 23
  4. 24
Monis Rasool Professor Asked on 28th August 2015 in Maths.
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1 Answer(s)

Answer: (3) 23

Explanation:-
tanθ + cotθ = 5 ………………. (1)
Square on both side,
(tanθ + cotθ)2 = 52
tan2θ + cot2θ + 2 tanθ cotθ = 25
tan2θ + cot2θ + 2 cotθ/cotθ = 25                  (tanθ = 1/cotθ)
tan2θ + cot2θ + 2 = 25
tan2θ + cot2θ  = 25 – 2
tan2θ + cot2θ = 23

Then, the tanθ + cotθ = 5, then tan2θ + cot2θ is 23.

Hence, the answer is (3) 23.

Anurag Mishra Professor Answered on 2nd September 2015.
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