Question

The value of $8184$ $\left[\sin {12}^o\sin {48}^o\sin {54}^o\right]+181[\tan {203}^o+\tan {22}^o+\tan {203}^o\tan {22}^o]$ is equal to

Answer 1

Consider, $8184\left[\sin {12}^o\sin {48}^o\sin {54}^o\right]+181[\tan {203}^o+\tan {22}^o+\tan {203}^o\tan {22}^o]$
$=4092\left[\cos \right({36}^0)-\cos ({60}^0\left)\right]\sin {54}^0+181\left[\tan \right({225}^0\left)\right(1-\tan {203}^0\tan {22}^0)+\tan {203}^0\tan {22}^0]$
$=4092[\cos {36}^0-\frac{1}{2}]\cos \left({36}^0\right)+181\left[1\right]$
$=4092(\frac{\sqrt{5}+1}{4}-\frac{1}{2})\left(\frac{\sqrt{5}+1}{4}\right)+181$
$=\frac{4816}{4}=1204$