Question

The value of $152.(\sin {30}^o+2{\cos }^2{45}^o+3\sin {30}^o+4{\cos }^2{45}^o+.....+17\sin {30}^o+18{\cos }^2{45}^o)$ is

• A. an integer but not a perfect square
• B. a rational number but not an integer
• C. $y^2$ for some positive integer $y$
• D. irrational

Answer 1

Answer: (A)

an integer but not a perfect square

$152(\sin 30+2{\cos }^{2}45+..........18{\cos }^{2}45)$
$=152(\frac{1}{2}+2.\frac{1}{2}+...18\frac{1}{2})=\frac{152}{2}(1+2+....18)=2^2.3^2.{\left(19\right)}^3$

Thus, on integer but not a perfect square.