TRIGONOMETRIC IDENTITIES AND GRAPHS OF INVERSE TRIGONOMETRIC RATIOS PYTHAGORAS THEOREM

FURTHER MATHEMATICS SSS2 FIRST TERM

WEEK 10

TRIGONOMETRIC IDENTITIES AND GRAPHS OF INVERSE TRIGONOMETRIC RATIOS PYTHAGORAS THEOREM

Example

If asinѳ + bcosѳ = p

andacosѳ – bsinѳ = q

show that a² + b² = p² + q²

 

Solution

asinѳ + bcosѳ = p                                         …(1)

acosѳ – bsinѳ = q                                          …(2)

Squaring both sides of (1)

          (asinѳ + bcos)² = p²

: a² sin²ѳ + 2absinѳ cosѳ + b²cos²ѳ = p²          …(3)

Squaring both sides of (2)

(acosѳ – bsinѳ)² = q²

a²cos²ѳ – 2absinѳ cosѳ + b²cos²ѳ = q²…