If x - a sin- and y - a cos- The value of y 2- x 2 is equal to-A- -2 aB- aC- a-2D- a2

The correct option is B a x = √(a) sinα and y = √(a) cosα x^2 = a sin^2α and y^2 = a cos^2α On adding x^2 and y^2, we get y^2 + x^2 = a(cos^2α + sin^2α) = a ...

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Standard X

Mathematics

Trigonometric Identities

If x =√ a sin...

Question

If $x = \sqrt{a} s i n α$ and $y = \sqrt{a} c o s α$ . The value of $y^{2}$ + $x^{2}$ is equal to .

\sqrt{2} a

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\frac{a}{2}

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a^{2}

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Solution

The correct option is B a
x = $\sqrt{a} s i n α$ and y = $\sqrt{a} c o s α$

$x^{2}$ = $a s i n^{2} α$ and $y^{2}$ = $a c o s^{2} α$
On adding $x^{2} a n d y^{2}$ , we get
$y^{2}$ $+$ $x^{2}$ = $a (c o s^{2} α + s i n^{2} α) = a$

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If x=√a sinα and y=√a cosα. The value of y2 + x2 is equal to .

The correct option is B a x = √a sinα and y = √a cosα x2 = a sin2α and y2 = a cos2α On adding x2 and y2, we get y2 + x2 = a(cos2α+sin2α)=a

If $x = \sqrt{a} s i n α$ and $y = \sqrt{a} c o s α$ . The value of $y^{2}$ + $x^{2}$ is equal to .

The correct option is B a
x = $\sqrt{a} s i n α$ and y = $\sqrt{a} c o s α$

$x^{2}$ = $a s i n^{2} α$ and $y^{2}$ = $a c o s^{2} α$
On adding $x^{2} a n d y^{2}$ , we get
$y^{2}$ $+$ $x^{2}$ = $a (c o s^{2} α + s i n^{2} α) = a$