What is the value of x, where 0 <= x < 30 deg satisfying tan 3x tan 6x = 1 ?
10°
We are given the equation:
tan(3x) * tan(6x) = 1
We need to find the value of x, where 0 ≤ x < 30°. One way to solve this is to recognize a useful identity from trigonometry:
tan(A) * tan(B) = 1 when A + B = 90° (or π/2 radians).
In our case, let:
3x + 6x = 90°
This simplifies to:
9x = 90°
Solving for x:
x = 90° / 9 = 10°
Thus, the value of x that satisfies the equation tan(3x) * tan(6x) = 1 is 10°.
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