Question

If x = a sec θ and y = b tan θ, thenb²x²-a²y² =
(a)ab
(b)a² − b²
(c)a² + b²
(d)a² b²

Answer 1

Answer:

The value of b²x² - a²y²  is a²b².

Among the given options option (d)  a²b²  is correct.  

Step-by-step explanation:

Given : x = a sec θ and y = b tanθ

On Substituting the values of x and y in the given expression b²x² - a²y²,  

b²x² -  a²y² = b²(a sec θ)² -  a²(b tan θ)²

= b²a²sec²θ -  a²b²tan²θ

= a²b²(sec²θ - tan²θ)

= a²b² × 1

[By using the identity , sec² θ -  tan² θ = 1]

b²x² -  a²y² = a²b²

Hence, the value of b²x² - a²y²  is a²b².

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Answer 2

Answer:

b² x² - a² y² = a² b²

Option a.  is correct .

Step-by-step explanation:

Given ;

x = a sec θ and y = b tan θ

Squaring both equation we get :

x² = a² sec² θ ... ( i )

y² = b² tan² θ ... ( ii )

Let ,

b² x²- a² y² =  p

Putting x² and y² values from ( i )  and  ( ii )  in p

p = b² a² sec² θ - a² b² tan² θ

p = a² b² sec² θ - a² b² tan² θ

Taking  a² b² as common we get

p = a² b² ( sec² θ - tan² θ )

We know ( sec² θ - tan² θ )  = 1

⇒ p =  a² b²

b² x² - a² y² = a² b²

Thus we get answer .