If x- a cosec- and y-b - then which of the following equations is true-A- x2-y2-a2-b2B- x2-a02-y2-b2-1C- x2-y2-a2-b2D- x2-a2-y2-b2-1

The correct option is B x^2/a^2 y^2/b^2 = 1 x = a cosec θ⇒x/a = cosec θ.....(1) y = b cot θ⇒y/b = cot θ.....(2) Squaring the equations and subtracting (2) fr ...

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Byju's Answer

Standard X

Mathematics

Trigonometric Identity- 2

If x= a cosec...

Question

If $x = a c o s e c θ$ and $y = b c o t θ$ , then which of the following equations is true ?

$x^{2} - y^{2} = a^{2} - b^{2}$

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$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$

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$x^{2} + y^{2} = a^{2} + b^{2}$

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$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

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Solution

The correct option is B
$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$

$x = a c o s e c θ \Rightarrow \frac{x}{a} = c o s e c θ$ .....(1)

$y = b c o t θ \Rightarrow \frac{y}{b} = c o t θ$ .....(2)

Squaring the equations and subtracting (2) from (1) we get,

$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = c o s e c^{2} θ - c o t^{2} θ$

$∴ \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1.... (1 + c o t^{2} θ = c o s e c^{2} θ)$

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If x=a cosec θ and y=b cot θ, then which of the following equations is true ?

The correct option is B x2a2−y2b2=1 x=a cosec θ⇒xa=cosec θ.....(1) y=b cot θ⇒yb=cot θ.....(2) Squaring the equations and subtracting (2) from (1) we get, x2a2−y2b2=cosec2θ−cot2θ ∴x2a2−y2b2=1....(1+cot2θ=cosec2θ)

If $x = a c o s e c θ$ and $y = b c o t θ$ , then which of the following equations is true ?