(0.0625−0.0625cosa0.2522)(\frac{0.0625 - 0.0625 cos a}{0.252^2}) + (1−0.345cosa0.654)2(\frac{1-0.345 cos a}{0.654})^2

asked by guest
on Jan 12, 2025 at 6:59 pm



You asked:

Evaluate the expression: 0.0625−0.0625cos⁡(a)0.2522+(1−0.345cos⁡(a)0.654)2\frac{0.0625 - 0.0625 \cos\left( a \right)}{{0.252}^{2}} + {\left( \frac{1 - 0.345 \cos\left( a \right)}{0.654} \right)}^{2}

MathBot Answer:

Evaluated



0.0625−0.0625cos⁡(a)0.2522+(1−0.345cos⁡(a)0.654)2=(500327−115cos⁡(a)218)2−15625cos⁡(a)15876+1562515876\displaystyle \frac{0.0625 - 0.0625 \cos\left( a \right)}{{0.252}^{2}} + {\left( \frac{1 - 0.345 \cos\left( a \right)}{0.654} \right)}^{2} = \left(\frac{500}{327} - \frac{115 \cos{\left(a \right)}}{218}\right)^{2} - \frac{15625 \cos{\left(a \right)}}{15876} + \frac{15625}{15876}

Expanded

0.0625−0.0625cos⁡(a)0.2522+(1−0.345cos⁡(a)0.654)2=13225cos⁡2(a)47524−489930625cos⁡(a)188622756+626640625188622756\frac{0.0625 - 0.0625 \cos\left( a \right)}{{0.252}^{2}} + {\left( \frac{1 - 0.345 \cos\left( a \right)}{0.654} \right)}^{2} = \frac{13225 \cos^{2}{\left(a \right)}}{47524} - \frac{489930625 \cos{\left(a \right)}}{188622756} + \frac{626640625}{188622756}

Factored

0.0625−0.0625cos⁡(a)0.2522+(1−0.345cos⁡(a)0.654)2=25⋅(2099601cos⁡2(a)−19597225cos⁡(a)+25065625)188622756\frac{0.0625 - 0.0625 \cos\left( a \right)}{{0.252}^{2}} + {\left( \frac{1 - 0.345 \cos\left( a \right)}{0.654} \right)}^{2} = \frac{25 \cdot \left(2099601 \cos^{2}{\left(a \right)} - 19597225 \cos{\left(a \right)} + 25065625\right)}{188622756}

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