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Question
If cos 9α = sin α and 9α < 90°, then the value of tan 5α is ______.
Options
`1/sqrt(3)`
`sqrt(3)`
1
0
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Solution
If cos 9α = sin α and 9α < 90°, then the value of tan 5α is 1.
Explanation:
According to the question,
cos 9α = sin α and 9α < 90°
i.e. 9α is an acute angle
We know that,
sin(90° – θ) = cos θ
So, cos 9α = sin(90° – α)
Since, cos 9α = sin(90° – 9α) and sin(90° – α) = sin α
Thus, sin(90° – 9α) = sin α
90° – 9α = α
10α = 90°
α = 9°
Substituting α = 9° in tan 5α, we get,
tan 5α = tan(5 × 9°)
= tan 45°
= 1
∴ tan 5α = 1
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