Question

(acotΘ +bcosecΘ)^2 -(acosecΘ +bcotΘ)^2= ?

Answer 1

Answer:

Step-by-step explanation:

acotθ + bCosecθ = p

bcotθ + aCosecθ = q

to find p*p - qq

= p² - q²

= (p + q) (p - q)

p + q = acotθ + bCosecθ + bcotθ + aCosecθ

= (a + b)cotθ + (a + b)Cosecθ

= (a + b)(cotθ + Cosecθ)

= (a + b) (Cosθ/Sinθ + 1/Sinθ)

= (a + b)(Cosθ+ 1)/Sinθ

p - q = acotθ + bCosecθ - bcotθ - aCosecθ

= (a - b)cotθ - (a - b)Cosecθ

= (a - b)(cotθ - Cosecθ)

= (a - b) (Cosθ/Sinθ - 1/Sinθ)

= (a - b)(Cosθ - 1)/Sinθ

(p + q) (p - q)

= (a + b)(Cosθ+ 1)/Sinθ   * (a - b)(Cosθ - 1)/Sinθ

= (a² - b²)(Cos²θ - 1)/Sin²θ

= (a² - b²)(-Sin²θ)/Sin²θ

= b² - a²

p*p - qq = b² - a²