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#### Monoxdifly

##### Well-known member

- Aug 6, 2015

- 284

a. 4π

b. 5π

c. 6π

d. 7π

e. 8π

What I've done thus far:

\(\displaystyle 2sin^2x\geq3cos2x+3\)

\(\displaystyle 2sin^2x\geq3(cos2x+1)\)

\(\displaystyle 2sin^2x\geq3(cos^2x-sin^2x+sin^2x+cos^2x)\)

\(\displaystyle 2sin^2x\geq3(2cos^2x)\)

\(\displaystyle sin^2x\geq3cos^2x\)

\(\displaystyle \frac{sin^2x}{cos^2x}\geq3\)

\(\displaystyle tan^2x\geq3\)

\(\displaystyle tanx\geq\sqrt3\)

\(\displaystyle tanx\geq tan60°\) or \(\displaystyle tanx\geq tan240°\)

Since the value of tangent become negative after 90° and 270° respectively, I assume that [a, b] ∪ [c, d] is [60°, 90°] ∪ [240°, 270°] thus a + b + c + d = 660° = \(\displaystyle 3\frac23\pi\), but it isn't in the options. Where did I do wrong? I'm sure I solved the inequation alright and just blundered in determining the intervals, but how should I fix them?