Question

if x = cosec theta and y = b sec theta prove that a^2/x^2 +x^2/y^2 = 1

Answer 1

Answer:

b²x² - a²y²  = a²b² if x =a secθ  y= b tanθ or if x =aCosecθ  y= bCotθ

Step-by-step explanation:

to be proved

b²x² - a²y²  = a²b²

Case i)

if x =a secθ  y= b tanθ

LHS = b²x² - a²y²

= b²(a secθ)² - a²(btanθ)²

= b²a² sec²θ - a²b²tan²θ

= a²b²( sec²θ - tan²θ)

as we know that sec²θ - tan²θ = 1

= a²b²

= RHS

Case iI)

if x =aCosecθ  y= b Cotθ

LHS = b²x² - a²y²

= b²(aCosecθ)² - a²(bCotθ)²

= b²a²Cosec²θ - a²b²Cot²θ

= a²b²( Cosec²θ - Cot²θ)

as we know that Cosec²θ - Cot²θ = 1

= a²b²

= RHS