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  • If cos 9α = sinα and 9α < 90° , then the value of tan5α is (A) 1 by sqroot 3 (B) sqroot 3(C) 1(D) 0

If cos 9α = sinα and 9α < 90° , then the value of tan5α is
  (A) \frac{1}{\sqrt{3}}            (B) {\sqrt{3}             (C) 1                (D) 0

Answers (1)

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Answer.          [C]                  
Solution.         Given :- cos 9\alpha = sin\alpha
cos9 \alpha = cos(90 – \alpha)
  \because (cos (90 – \alpha) = sin\alpha)
  9\alpha = 90 – \alpha
9\alpha+ \alpha = 90
10 \alpha= 90
\alpha = \frac{90}{10}
Now tan 5\alpha is
Put \alpha = 9 we get
tan 5\times (9)
tan 450
= 1
{\because from the table of trigonometric ratios of angles we know that tan 450 = 1}
Hence option C is correct.

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infoexpert27

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