Question

The value of $\frac{{\cos }^2{56}^o+{\cos }^2{34}^o}{{\sin }^2{56}^o+{\sin }^2{34}^o}+3{\tan }^2{56}^o{\tan }^2{34}^o$ is :

• A. $1$
• B. $4$
• C. $2$
• D. $3$

Answer 1

The correct option is B $4$

The value of $\frac{{\cos }^2{56}^o+{\cos }^2{34}^o}{{\sin }^2{56}^o+{\sin }^2{34}^o}+3{\tan }^2{56}^o{\tan }^2{34}^o$ is
$=\frac{{\cos }^2{56}^o+{\cos }^2({90}^o-{56}^o)}{{\sin }^2({90}^o-{34}^o)+{\sin }^2{34}^o}+3{\tan }^2({90}^o-{34}^o){\tan }^2{34}^o$
$=\frac{{\cos }^2{56}^o+{\sin }^2{56}^o}{{\cos }^2{34}^o+{\sin }^2{34}^o}+3{\cot }^2{34}^o{\tan }^2{34}^o$
$=\frac{1}{1}+3\times \frac{1}{{\tan }^2{34}^o}\times {\tan }^2{34}^o=1+3\times 1=4$

Hence, option B is correct.