Question

If x= a cos theta, y = b sin theta, then show that x^2/a^2 + y^2/b^2 =1

Answer 1

Given---> x = a Cosθ , y = b Sinθ

To show----> x² / a² + y² / b² = 1

Solution----> ATQ,

x = a Cosθ

=> x / a = Cosθ -------------------( 1 )

y = b Sinθ

=> y / b = Sinθ ........................ ( 2 )

We know that,

Cos²θ + Sin²θ = 1

=> ( x / a )² + ( y / b )² = 1

=> x² / a² + y² / b² = 1

=> x² / a² + y² / b² = 1

Additional information---->

1) 1 + tan²θ = Sec²θ

2) 1 + Cot²θ = Cosec²θ

3) Sin ( 90° - θ ) = Cosθ

4) Cos ( 90° - θ ) = Sinθ

5) tan ( 90° - θ ) = Cotθ

6) Cot( 90° - θ ) = tanθ

7) Sec ( 90° - θ ) = Cosecθ

8) Cosec ( 90° - θ ) = Secθ