turkey-yks 2019 Q33

turkey-yks · Other · yks-ayt Trig Proofs Trigonometric Identity Simplification
Two right triangles $A B C$ and $B C D$ with one side coinciding are drawn as shown in the figure, and the resulting two regions are painted yellow and blue.
$$\mathrm { m } ( \widehat { \mathrm { DCA } } ) = \mathrm { m } ( \widehat { \mathrm { BAC } } ) = \mathrm { x }$$
Accordingly, what is the expression in terms of x for the ratio of the area of the yellow region to the area of the blue region?
A) $\sin 2 x$
B) $\cos 2 x$
C) $\sin ^ { 2 } x$
D) $\cot ^ { 2 } x$
E) $\csc ^ { 2 } x$
Two right triangles $A B C$ and $B C D$ with one side coinciding are drawn as shown in the figure, and the resulting two regions are painted yellow and blue.

$$\mathrm { m } ( \widehat { \mathrm { DCA } } ) = \mathrm { m } ( \widehat { \mathrm { BAC } } ) = \mathrm { x }$$

Accordingly, what is the expression in terms of x for the ratio of the area of the yellow region to the area of the blue region?\\
A) $\sin 2 x$\\
B) $\cos 2 x$\\
C) $\sin ^ { 2 } x$\\
D) $\cot ^ { 2 } x$\\
E) $\csc ^ { 2 } x$