If sin-1x- - and sin-1y- - then 1-xy-

Explanation for the correct option.Given that, sin^ 1(x)=θ +β and sin^ 1(y)=θ β.⇒ x=sin(θ +β ) and y=sin(θ β )1+xy=1+sin(θ +β )sin(θ β )0ex0ex1+xy=1+sin^2θ ...

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Standard XI

Mathematics

Geometrical Representation of Argument and Modulus

If sin-1x=θ +...

Question

If $\sin^{- 1} (x) = θ + β$ and $\sin^{- 1} (y) = θ - β$ , then $1 + x y =$

$\sin^{2} θ + \sin^{2} β$

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$\sin^{2} θ + \cos^{2} β$

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$\cos^{2} θ + \cos^{2} β$

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$\cos^{2} θ + \sin^{2} β$

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Solution

The correct option is B
$\sin^{2} θ + \cos^{2} β$

Explanation for the correct option.
Given that, $\sin^{- 1} (x) = θ + β$ and $\sin^{- 1} (y) = θ - β$ .
$\Rightarrow x = \sin (θ + β) and y = \sin (θ - β)$
$1 + x y = 1 + \sin (θ + β) \sin (θ - β) 1 + x y = 1 + \sin^{2} θ - \sin^{2} β$
Using the identity, $\sin^{2} A + \cos^{2} A = 1$ .
$1 + x y = \sin^{2} θ + \cos^{2} β$
Hence, option B is correct.

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If sin-1(x)=θ+β and sin-1(y)=θ-β, then 1+xy=

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