Question

Evaluate : ${\sin }^{2}90.{\cos }^{2}45+4{\tan }^{2}30+\frac{1}{2}{\sin }^{2}a-2{\cos }^{2}90+\frac{1}{24}$

Answer 1

Consider the given expression.

$\Rightarrow {\sin }^2{90}^0{\cos }^2{45}^0+4{\tan }^{2}30+\frac{1}{2}{\sin }^{2}a-2{\cos }^2{90}^0+\frac{1}{24}$

Put the value of all trigonometry function in given expression, we get

$\Rightarrow {\sin }^2{90}^0{\cos }^2{45}^0+4{\tan }^{2}30+\frac{1}{2}{\sin }^{2}a-2{\cos }^2{90}^0+\frac{1}{24}$

$\Rightarrow {\left(1\right)}^2.{\left(\frac{1}{\sqrt{2}}\right)}^2+4.{\left(\frac{1}{\sqrt{3}}\right)}^2+\frac{1}{2}{\sin }^{2}a-2{\left(0\right)}^2+\frac{1}{24}$

$\Rightarrow \frac{1}{2}+\frac{4}{3}+\frac{1}{2}{\sin }^{2}a+\frac{1}{24}$

$\Rightarrow \frac{1}{2}{\sin }^{2}a+\frac{12+32+12}{24}$

$\Rightarrow \frac{1}{2}{\sin }^{2}a+\frac{56}{24}$

$\Rightarrow \frac{1}{2}{\sin }^{2}a+\frac{7}{3}$

Hence, this is the answer.