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Mathematics

cos θ. cos (90° - θ)tan (90° - θ)\dfrac{\text{cos θ. cos (90° - θ)}}{\text{tan (90° - θ)}} is equivalent to :

  1. cos2 θ - 1

  2. sin2 θ

  3. sin2 θ - cos2 θ

  4. sin2 θ - 1

Trigonometric Identities

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Answer

Solving,

cos θ. cos (90° - θ)tan (90° - θ)cos θ . sin θcot θcos θ . sin θcos θsin θcos θ . sin θ . sin θcos θsin2θ.\Rightarrow \dfrac{\text{cos θ. cos (90° - θ)}}{\text{tan (90° - θ)}} \\[1em] \Rightarrow \dfrac{\text{cos θ . sin θ}}{\text{cot θ}} \\[1em] \Rightarrow \dfrac{\text{cos θ . sin θ}}{\dfrac{\text{cos θ}}{\text{sin θ}}} \\[1em] \Rightarrow \dfrac{\text{cos θ . sin θ . sin θ}}{\text{cos θ}} \\[1em] \Rightarrow \text{sin}^2 θ.

Hence, Option 2 is the correct option.

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