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Solve: cosx(tanx + sqroot3) - sqroot3/2(tanx-sqroot3)
Provide exact answers .. help
cosx(tanx + sqroot3) - sqroot3/2(tanx-sqroot3) = What ?
Well, 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
tan2x + 2√3 tanx + 3 = 3/4 (tan2x - 2√3 tanx + 3)(tan2x + 1)
Let u = tanx to unclutter things. You end up needing to solve
3u4 - 9√3 u3 + 8u2 - 14√3 u + 6 = 0
Good luck. Maybe the original problem is missing something.
To simplify the expression cosx(tanx + √3) - √3/2(tanx - √3), you can follow these steps:
Step 1: Distribute the cosine term by multiplying it with each term inside the parentheses.
cosx(tanx + √3) - √3/2(tanx - √3)
= cosx * tanx + cosx * √3 - (√3/2) * tanx + (√3/2) * √3
Step 2: Simplify any trigonometric ratios.
Recall that tanx = sinx/cosx.
= cosx * (sinx/cosx) + cosx * √3 - (√3/2) * (sinx/cosx) + (√3/2) * √3
= sinx + cosx * √3 - (√3/2) * sinx/cosx + (√3/2) * √3
Step 3: Combine like terms.
= sinx - (√3/2) * sinx/cosx + cosx * √3 + (√3/2) * √3
= sinx - (√3/2) * (sinx/cosx) + cosx * √3 + (√3/2) * √3
Step 4: Simplify the trigonometric ratio.
= sinx - (√3/2) * tanx + cosx * √3 + (√3/2) * √3
= sinx - (√3/2) * tanx + cosx * √3 + (√3/2) * √3
Now, this is the simplified expression: sinx - (√3/2) * tanx + cosx * √3 + (√3/2) * √3.
Please note that we have simplified the expression and provided the exact answer, but we have not solved for a specific value of x.