(-3tant-2tan2t) / (3cott-2tan2t)

asked by guest
on Jan 31, 2025 at 9:22 pm



You asked:

Evaluate the expression: −(3tan⁡(t))−2tan⁡(2t)3cot⁡(t)−2tan⁡(2t)\frac{-\left( 3 \tan\left( t \right) \right) - 2 \tan\left( 2 t \right)}{3 \cot\left( t \right) - 2 \tan\left( 2 t \right)}

MathBot Answer:

Evaluated



−(3tan⁡(t))−2tan⁡(2t)3cot⁡(t)−2tan⁡(2t)=−2tan⁡(2t)−3tan⁡(t)−2tan⁡(2t)+3cot⁡(t)\displaystyle \frac{-\left( 3 \tan\left( t \right) \right) - 2 \tan\left( 2 t \right)}{3 \cot\left( t \right) - 2 \tan\left( 2 t \right)} = \frac{- 2 \tan{\left(2 t \right)} - 3 \tan{\left(t \right)}}{- 2 \tan{\left(2 t \right)} + 3 \cot{\left(t \right)}}

Expanded

−(3tan⁡(t))−2tan⁡(2t)3cot⁡(t)−2tan⁡(2t)=−2tan⁡(2t)−2tan⁡(2t)+3cot⁡(t)−3tan⁡(t)−2tan⁡(2t)+3cot⁡(t)\frac{-\left( 3 \tan\left( t \right) \right) - 2 \tan\left( 2 t \right)}{3 \cot\left( t \right) - 2 \tan\left( 2 t \right)} = - \frac{2 \tan{\left(2 t \right)}}{- 2 \tan{\left(2 t \right)} + 3 \cot{\left(t \right)}} - \frac{3 \tan{\left(t \right)}}{- 2 \tan{\left(2 t \right)} + 3 \cot{\left(t \right)}}

Factored

−(3tan⁡(t))−2tan⁡(2t)3cot⁡(t)−2tan⁡(2t)=−2tan⁡(2t)+3tan⁡(t)−2tan⁡(2t)+3cot⁡(t)\frac{-\left( 3 \tan\left( t \right) \right) - 2 \tan\left( 2 t \right)}{3 \cot\left( t \right) - 2 \tan\left( 2 t \right)} = - \frac{2 \tan{\left(2 t \right)} + 3 \tan{\left(t \right)}}{- 2 \tan{\left(2 t \right)} + 3 \cot{\left(t \right)}}

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