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Two statements are given: Statement I: If \(\theta\) is acute and \(\sin (\theta)=\frac{5}{13}\), then the value of \(\tan (\theta)=\frac{5}{12}\) Statement II: If \(\theta\) is acute and \(\cot…

Question and options

Two statements are given:

Statement I: If θ\theta is acute and sin⁡(θ)=513\sin (\theta)=\frac{5}{13}, then the value of tan⁡(θ)=512\tan (\theta)=\frac{5}{12}

Statement II: If θ\theta is acute and cot⁡(θ)=125\cot (\theta)=\frac{12}{5}, then the value of sin⁡(θ)=512\sin (\theta)=\frac{5}{12}

In the light of the given statements, choose the correct answer from the given options:
  1. Both Statement I and Statement II are true
  2. Both Statement I and Statement II are false
  3. Statement I is true but Statement II is false
  4. Statement I is false but Statement II is true

Answer and explanation

Correct answer: C - Statement I is true but Statement II is false
I: theta acute, sin = 5/13 gives cos = 12/13, so tan = 5/12 (true). II: cot = 12/5 gives sin = 5/13, not 5/12 (false).

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