What is (\frac{\cos \theta-\sin \theta+1}{\cos \theta+\sin \theta-1})(\cot \theta-\csc \theta) equal to?

Explanation

Rewrite the first term by dividing the numerator and denominator by \sin \theta: \frac{\cot \theta - 1 + \csc \theta}{\cot \theta + 1 - \csc \theta}, which simplifies directly to \cot \theta + \csc \theta. Multiplying this by (\cot \theta - \csc \theta) gives \cot^2 \theta - \csc^2 \theta = -1.

Related questions on Trigonometry

• Two poles are situated 24 m apart and their heights differ by 10 m. What is the distance between their tips?
• If \frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4, then which one of the following is a value of $(\tan^2 \...
• For 0 < \theta < \frac{\pi}{2}, consider the following : I. $(\tan^4 \theta + \tan^6 \theta)(\cot^4 \theta + \cot^6 \theta) = \sec^2 \the...
• If 3\sin \theta + 4\cos \theta = 5, then what is a value of 4\tan \theta + 3\cot \theta ?
• At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be \frac{5}{6}. On walking 70 m toward...