Theory question 104
TrigonometryIf sin X = (p − q)/(p + q), where 0° ≤ X ≤ 90°, find 1 − tan2X.
Show the model answer
Model answer
Opposite p − q, hypotenuse p + q, adjacent √((p + q)² − (p − q)²) = 2√(pq).
tan²X = (p − q)²/(4pq).
1 − tan²X = (4pq − (p − q)²)/(4pq) = (6pq − p² − q²)/(4pq).
Explanation
Draw a right triangle and use Pythagoras for the third side.