Discussion
In a right angled triangle ABC, right angle is at B. If cotA = 1, then which of the following option is false ?
Answer: B
The false option is \(\cos A = \sqrt{2}\).
\(\cot A = 1\) means \(A = 45^{\circ}\), so \(\sin A = \cos A = \frac{1}{\sqrt{2}}\). The cosine of an angle can never exceed 1, so \(\sqrt{2} \approx 1.414\) is impossible.
The other three are true: \(\sin A = \frac{1}{\sqrt{2}}\); \(\tan A + \cot A = 1 + 1 = 2\); and \(\cos A\,\text{cosec}\,A = \cos A/\sin A = \cot A = 1\).
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