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Question
The value of `(1 - tan^2 15^circ)/(1 + tan^2 15^circ)` is ______.
Options
1
`sqrt(3)`
`sqrt(3)/2`
2
Solution
The value of `(1 - tan^2 15^circ)/(1 + tan^2 15^circ)` is `bbunderline(sqrt3/2)`.
Explanation:
Given that: `(1 - tan^2 15^circ)/(1 + tan^2 15^circ)`
Let θ = 15°
∴ 2θ = 30°
cos 2θ = `(1 - tan^2 theta)/(1 + tan^2 theta)`
⇒ cos 3θ = `(1 - tan^2 15^circ)/(1 + tan^2 15^circ)`
⇒ `sqrt(3)/2 = (1 - tan^2 15^circ)/(1 + tan^2 15^circ)`
= `sqrt3/2`
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