Trigonometrical Equations 3 Question 12

13. The number of values of θ in the interval π2,π2 such that θnπ5 for n=0,±1,±2 and tanθ=cot5θ as well as sin2θ=cos4θ is……

(2010)

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Answer:

Correct Answer: 13. 3

Solution:

  1. Given, tanθ=cot5θ

tanθ=tanπ25θπ25θ=nπ+θ6θ=π2nπθ=π12nπ6 Also, cos4θ=sin2θ=cosπ22θ4θ=2nπ±π22θ

Taking positive sign,

6θ=2nπ+π2θ=nπ3+π12

Taking negative sign,

2θ=2nππ2θ=nππ4

Above values of θ suggest that there are only 3 common solutions.



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