If a cot theta+ b cosec theta=p and b cot theta+a consecutive theta =q then find p*p- q*q
Answers
Answer:
b² - a²
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
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