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April 19, 2014

Posted by **Don** on Monday, November 7, 2011 at 11:09pm.

Solve: cosx(tanx + sqroot3) - sqroot3/2(tanx-sqroot3)

Provide exact answers .. help

- Math C30 -
**Anonymous**, Monday, November 7, 2011 at 11:49pmcosx(tanx + sqroot3) - sqroot3/2(tanx-sqroot3) = What ?

- Math C30 -
**Steve**, Tuesday, November 8, 2011 at 11:41amWell, if you want

cosx(tanx + sqroot3) - sqroot3/2(tanx-sqroot3) = 0

rearrange things a bit to get

tanx + √3 = √3/2 (tanx - √3)*secx

square both sides to get

tan^{2}x + 2√3 tanx + 3 = 3/4 (tan^{2}x - 2√3 tanx + 3)(tan^{2}x + 1)

Let u = tanx to unclutter things. You end up needing to solve

3u^{4}- 9√3 u^{3}+ 8u^{2}- 14√3 u + 6 = 0

Good luck. Maybe the original problem is missing something.

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