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Question

$$\displaystyle \frac{\sin 36^{\circ}}{\cos 54^{\circ}}$$ = ___ 


A
0
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B
1
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C
23
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D
32
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Solution

The correct option is C $$1$$
We know that $$ \sin {(A)} = \cos \left(\dfrac{\pi}{2} - A\right) $$ where $$ \dfrac{\pi}{2}= 90^{o} $$

As $$ 54^{o}  = 90^{o} - 36^{o}  $$
we have $$ \dfrac {\sin (36^{o} )}{ \cos (54^{o})} =  \dfrac {\cos (54^{o} )}{ \cos (54^{o})} = 1 $$

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