Question

Could I get some help with this question on Trigonometric Identities?

Answer 1

$\bf 1-\cfrac{tan(\theta )cos(\theta )}{csc(\theta )}\implies 1-\cfrac{\frac{sin(\theta )}{cos(\theta )}cos(\theta )}{csc(\theta )} \\\\\\ \boxed{1-\cfrac{\frac{sin(\theta )}{\underline{cos(\theta )}}\cdot \underline{cos(\theta )}}{\frac{1}{sin(\theta )}}\implies 1-\cfrac{sin(\theta )}{\frac{1}{sin(\theta )}}}\implies 1-sin(\theta )sin(\theta )$