If 4 cos ²θ-1 =0, where θ is an acute angle, the value of 1 + tan2θ is
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If 4 cos ²θ-1 =0, where θ is an acute angle, the value of 1 + tan2θ is
If 4 cos ²θ-1 =0, where θ is an acute angle, the value of 1 + tan2θ is
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Answer:
theta belongs to 1st quadrant
[tex]4 \cos {}^{2} ( theta ) = 1 \\ \cos( theta ) = \frac{1}{2} \\ theta = 60[/tex]
now find the value of 1+tan2theta
[tex]1 + \tan(2 \times 60) \\ = 1 + \tan(120) = 1 + \tan(90 + 30) \\ = 1 - \cot(30) = 1 - \sqrt{3} [/tex]
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