Question

If sectheta =2x & ytantheta=2 then2(x^2-1/y^2)​

Answer 1

Answer :

Given that,

x = a secθ and y = b tanθ

Now, b²x² - a²y²

= b²(a secθ)² - a²(b tanθ)²

= b²(a² sec²θ) - a²(b² tan²θ)

= a²b² sec²θ - a²b² tan²θ

= a²b² (sec²θ - tan²θ)

= a²b² [∵ sec²θ - tan²θ = 1]

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Answer 2

Answer:

secθ=2x  ,   ytanθ=2

⇒sec2θ=4x2&y2tan2θ=4

⇒sec2θ=2.2x2&tan2θ=y24=2.y22

⇒2x2=21sec2θ&y22=21tan2θ

⇒ Now, 2[x2−y21]=2x2−y22

                                  =21sec2θ−21tan2