(2TAN45°+SEN30°+2COT53°)(SEC53°-TAN53°)

asked by guest
on Oct 24, 2024 at 4:11 pm



You asked:

Evaluate the expression: \(\left(2 \cdot \tan\left( 45^{\circ} \right) + \sin\left( 30^{\circ} \right) + 2 \cdot \cot\left( 53^{\circ} \right)\right) \cdot \left(\sec\left( 53^{\circ} \right) - \tan\left( 53^{\circ} \right)\right)\)

MathBot Answer:

Evaluated



\(\displaystyle \left(2 \cdot \tan\left( 45^{\circ} \right) + \sin\left( 30^{\circ} \right) + 2 \cdot \cot\left( 53^{\circ} \right)\right) \cdot \left(\sec\left( 53^{\circ} \right) - \tan\left( 53^{\circ} \right)\right) = \left(- \tan{\left(\frac{53 \pi}{180} \right)} + \sec{\left(\frac{53 \pi}{180} \right)}\right) \left(2 \cot{\left(\frac{53 \pi}{180} \right)} + \frac{5}{2}\right) \)

Expanded

\[\left(2 \cdot \tan\left( 45^{\circ} \right) + \sin\left( 30^{\circ} \right) + 2 \cdot \cot\left( 53^{\circ} \right)\right) \cdot \left(\sec\left( 53^{\circ} \right) - \tan\left( 53^{\circ} \right)\right) = - \sin{\left(30 ^\circ \right)} \tan{\left(53 ^\circ \right)} + \sin{\left(30 ^\circ \right)} \sec{\left(53 ^\circ \right)} - 2 \tan{\left(45 ^\circ \right)} \tan{\left(53 ^\circ \right)} + 2 \tan{\left(45 ^\circ \right)} \sec{\left(53 ^\circ \right)} - 2 \tan{\left(53 ^\circ \right)} \cot{\left(53 ^\circ \right)} + 2 \cot{\left(53 ^\circ \right)} \sec{\left(53 ^\circ \right)}\]

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