InterviewSolution
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InterviewSolution
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What is the value of \(\dfrac{\sin \theta + \cos \theta - \tan \theta}{\sec \theta + \text{cosec} \ \theta - \cot \theta}\) when \(\theta = \dfrac{3\pi}{4} ?\) |
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Answer» Correct Answer - Option 2 : 1 Concept: In the first quadrant, the values for sin, cos and tan are positive. In the second quadrant, the values for sin and cosec are positive only. In the third quadrant, the values for tan are positive only. In the fourth quadrant, the values for cos are positive only. sin(π - θ) = sin θ
Calculation: Here, \(\dfrac{\sin \theta + \cos \theta - \tan \theta}{\sec \theta + \text{cosec} \ \theta - \cot \theta}\)and \(\theta = \dfrac{3\pi}{4} =\pi -\frac \pi 4\) \(\rm \dfrac{\sin \theta + \cos \theta - \tan \theta}{\sec \theta + \text{cosec} \ \theta - \cot \theta}=\)\(\dfrac{\sin (\pi -\frac \pi 4)+ \cos(\pi -\frac \pi 4) - \tan(\pi -\frac \pi 4)}{\sec (\pi -\frac \pi 4) + \text{cosec} \ (\pi -\frac \pi 4) - \cot (\pi -\frac \pi 4)}\) \(=\dfrac{\sin (\frac \pi 4)- \cos( \frac \pi 4) + \tan(\frac \pi 4)}{-\sec (\frac \pi 4) + \text{cosec} \ (\frac \pi 4) +\cot (\frac \pi 4)}\) \(=\frac{\frac{1}{\sqrt2}-\frac{1}{\sqrt2}+1}{-\sqrt2+\sqrt2+1}\) = 1 Hence, option (2) is correct. |
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