Question : Evaluate the given expression: $\cos ^2 36^{\circ}+\cos 54^{\circ} \cdot \sin 36^{\circ}+\left(\frac{\tan 26^{\circ}}{\cot 64^{\circ}}\right)$
Option 1: 4
Option 2: 3
Option 3: 1
Option 4: 2
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Correct Answer: 2
Solution :
Given, $\cos ^2 36°+\cos 54° \cdot \sin 36°+\left(\frac{\tan 26°}{\cot 64°}\right)$
= $\cos^2 36°+\cos(90°-36°)\cdot\sin36°+\frac{\tan 26°}{\cot(90°-26°)}$
= $\cos^2 36° + \sin 36°\cdot \sin 36° + \frac{\tan 26°}{\tan 26°}$
= $1+1$ [$\because \sin^2x+\cos^2x = 1$]
= $2$
Hence, the correct answer is 2.
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