Question

Solve it urgently [Trigonometry Class X]

Answer 1

here is the answer hope it helps u

Answer 2

Hi !

x = a secθ + b tanθ 
y = a tanθ  + b secθ 

LHS = x² - y²
  
(a secθ  + b tanθ )² - (a tanθ  + b secθ )²

a²sec²θ  + 2ab secθ tanθ + b²tan²θ  - (a²tan²θ  + 2ab secθ tanθ  + b²sec²θ )

a²sec²θ  + 2ab secθ tanθ + b²tan²θ  - a²tan²θ - 2ab secθ tanθ - b²sec²θ

a²sec²θ - a²tan²θ +  b²tan²θ - b²sec²θ

a²(sec²θ - tan²θ ) + b²(tan²θ -sec²θ)

we know that ,
sec²θ - tan²θ = 1
tan²θ -sec²θ = -1

a²(1)  + b²( -1)

= a² - b²
 
= LHS