Question : $\cos^{2} 35^{\circ} + \cos 55^{\circ} \cdot \sin 35^{\circ} + \frac{\tan 34^{\circ}}{\cot 56^{\circ}} =$ ________.
Option 1: 2
Option 2: 3
Option 3: 4
Option 4: 1

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Question : The value of $\frac{4 \tan^{2} 30^{\circ} + \sin^{2} 30^{\circ} \cos^{2} 45^{\circ} + \sec^{2} 48^{\circ} - \cot^{2} 42^{\circ}}{\cos 37^{\circ} \sin 53^{\circ} + \sin 37^{\circ} \cos 53^{\circ} + \tan 18^{\circ} \tan 72^{\circ}}$ is:

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Answer 1

Correct Answer: 2

Solution : We know that $\sin θ = \cos (90 ° - θ)$
And, $\tan θ = \cot (90 ° - θ)$
So, $\cos^{2} 35^{\circ} + \cos 55^{\circ} \cdot \sin 35^{\circ} + \frac{\tan 34^{\circ}}{\cot 56^{\circ}}$
= $\cos^{2} 35^{\circ} + \cos (90^{\circ} - 35^{\circ}) \cdot \sin 35^{\circ} + \frac{\tan (90^{\circ} - 56^{\circ})}{\cot 56^{\circ}}$
= $\cos^{2} 35^{\circ} + \sin 35^{\circ} \cdot \sin 35^{\circ} + \frac{\cot 56^{\circ}}{\cot 56^{\circ}}$
= $\cos^{2} 35^{\circ} + \sin^{2} 35^{\circ} + \frac{\cot 56^{\circ}}{\cot 56^{\circ}}$
= $1 + 1$
= $2$
Hence, the correct answer is 2.

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Question : cos2⁡35∘+cos⁡55∘⋅sin⁡35∘+tan⁡34∘cot⁡56∘=________.Option 1: 2Option 2: 3Option 3: 4Option 4: 1

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Question : $\cos^{2} 35^{\circ} + \cos 55^{\circ} \cdot \sin 35^{\circ} + \frac{\tan 34^{\circ}}{\cot 56^{\circ}} =$ ________.
Option 1: 2
Option 2: 3
Option 3: 4
Option 4: 1