Question

What is the value of $\frac{{\cos }^2{56}^{\circ }+{\cos }^2{34}^{\circ }}{{\sin }^2{56}^{\circ }+{\sin }^2{34}^{\circ }}+3{\tan }^2{56}^{\circ }\times {\tan }^2{34}^{\circ }$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D 4

$\begin{array}{cc}\frac{{\cos }^2{56}^{\circ }+{\cos }^2{34}^{\circ }}{{\sin }^2{56}^{\circ }+{\sin }^2{34}^{\circ }}+3{\tan }^2{56}^{\circ }\times {\tan }^2{34}^{\circ }& =\frac{{\sin }^2({90}^{\circ }-{56}^{\circ })+{\cos }^2{34}^{\circ }}{{\cos }^2({90}^{\circ }-{56}^{\circ })+{\sin }^2{34}^{\circ }}+3{\cot }^2({90}^{\circ }-{56}^{\circ })\times {\tan }^2{34}^{\circ }\\ & =\frac{{\sin }^2{34}^{\circ }+{\cos }^2{34}^{\circ }}{{\cos }^2{34}^{\circ }+{\sin }^2{34}^{\circ }}+3{\cot }^2{34}^{\circ }\times {\tan }^2{34}^{\circ }\\ & =1+3\\ & =4\end{array}$