Question

If \(\cos\theta\cosec\theta=-1\) and \(\theta\) lies in the second quadrant, then \(\cos\theta=\)

• A. \(-\frac{\sqrt{3}}{2}\)
• B. \(\frac{\sqrt{2}}{2}\)
• C. \(-\frac{\sqrt{2}}{2}\)
• D. \(-\sqrt{2}\)

Hint:

In the second quadrant, sine is positive and cosine is negative. If \(\tan\theta=-1\), then \(\theta=135^\circ\), so \(\cos\theta=-\frac{\sqrt{2}}{2}\).

Answer 1

The Correct Option is C