Question

Approach

Step-by-step working

1. 1

   LHS $=({\tan }^2\theta +1)+({\cot }^2\theta +1)={\sec }^2\theta +{\csc }^2\theta$

   1 mark
2. 2

   $=\frac{1}{{\cos }^2\theta }+\frac{1}{{\sin }^2\theta }$

   0.5 marks
3. 3

   $=\frac{{\sin }^2\theta +{\cos }^2\theta }{{\cos }^2\theta {\sin }^2\theta }=\frac{1}{{\cos }^2\theta {\sin }^2\theta }$

   1 mark
4. 4

   $={\sec }^2\theta {\csc }^2\theta =$ RHS

   0.5 marks

Concepts used