Question

Sin (90-theta) into Cos(90-theta)=Cot theta/1+cot square theta

Answer 1

$sin(90 - x)cos(90 - x) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{cotx}{1 + {cot}^{2} x} \\ cosx \times sinx = \frac{cosx}{sinx \times {cosec}^{2} x} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{cos}{sinx} \\ {sin}^{2} x = 1 \\ sinx = 1 or \: sinx = - 1\\ x = 90 \: or \: x = 270 \\ here \: \: x = theta$