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3sin 47°cos 43°tan 50°cot 40°2 sin245°3\dfrac{\text{sin 47°}}{\text{cos 43°}} - \dfrac{\text{tan 50°}}{\text{cot 40°}} - \text{2 sin}^2 45° is equal to :

  1. 0

  2. -1

  3. 1

  4. 2

Trigonometric Identities

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Answer

Solving,

3sin 47°cos 43°tan 50°cot 40°2 sin245°3sin 47°cos (90° - 47°)tan 50°cot (90° - 50°)2 sin245°3sin 47°sin 47°tan 50°tan 50°2×(12)23×112×123111.\Rightarrow 3\dfrac{\text{sin 47°}}{\text{cos 43°}} - \dfrac{\text{tan 50°}}{\text{cot 40°}} - \text{2 sin}^2 45° \\[1em] \Rightarrow 3\dfrac{\text{sin 47°}}{\text{cos (90° - 47°)}} - \dfrac{\text{tan 50°}}{\text{cot (90° - 50°)}} - \text{2 sin}^2 45° \\[1em] \Rightarrow 3\dfrac{\text{sin 47°}}{\text{sin 47°}} - \dfrac{\text{tan 50°}}{\text{tan 50°}} - 2 \times \Big(\dfrac{1}{\sqrt{2}}\Big)^2 \\[1em] \Rightarrow 3 \times 1 - 1 - 2 \times \dfrac{1}{2} \\[1em] \Rightarrow 3 - 1 - 1 \\[1em] \Rightarrow 1.

Hence, Option 3 is the correct option.

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