Question

Without using trigonometric tables, prove that:

cosec²72° − tan²18° = 1

Answer 1

LHS = cosec²72° − tan²18°

= cosec² (`90^circ - 18^circ`) - tan² `18^circ`

= `sec^2 18^circ` - tan² `18^circ`

= 1

= RHS