Question

Eliminate 0 from the x=3sec0, y=4tan0​

Answer 1

Step-by-step explanation:

Given :-

x=3sec0, y=4tan0

To find:-

Eliminate 0 from the x=3sec0, y=4tan0

Solution:-

Given equations are

x=3sec0

On squaring both sides then

=>x^2= (3 Sec 0)^2

=> x^2 = 9 Sec^2 0

=>x^2/9 = Sec^2 0---------(1)

and

y=4tan0

On squaring both sides then

=>y^2 = (4 tan0)^2

=>y^2 = 16 tan^2 0

=>y^2/16 = Tan^2 0--------(2)

On subtracting (2) from (1) then

=> Sec^2 0 - Tan^2 0 = (x^2/9)-(y^2/16)

We know that

Sec^2 A -Tan^2 A = 1

=> (x^2/9)-(y^2/16) = 1

(or)

LCM of 9 and 16 = 144

=> (16x^2-9y^2)/144 = 1

=> 16x^2-9y^2 = 144

Answer:-

The answer for the given problem is

(x^2/9)-(y^2/16) = 1 (or) 16x^2-9y^2 = 144

Used formula:-

• Sec^2 A -Tan^2 A = 1