Calculate -a2 - b2 if x - 0- a - xcos- and b - xsin-

The correct option is B x We need to find √( a ^ 2 + b ^ 2 ) Given, a = xcosθ and b =x sinθ #160; ∴√(a^2+b^2) =√( xcosθ^ 2 + xsinθ^ ...

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Sign of Trigonometric Ratios in Different Quadrants

Calculate √...

Question

Calculate $\sqrt{a^{2} + b^{2}}$ if $x > 0, a = x cos θ$ , and $b = x sin θ$

1

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x

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2 x

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x (cos θ + sin θ)

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x cos θ sin θ

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If $x c o s θ - y s i n θ = a$ and $x s i n θ + y c o s θ = b,$ then $\frac{x^{2} + y^{2}}{a^{2} + b^{2}}$ = ___.

x cos θ - y sin θ = a, x sin θ + y cos θ = b

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

∣ ∣ ∣ ∣ ∣ \begin{matrix} 3 x^{2} & x^{2} + x c o s θ + c o s^{2} θ & x^{2} + x s i n θ + s i n^{2} θ x^{2} + x c o s θ + c o s^{2} θ & 3 c o s^{2} θ & 1 + \frac{s i n 2 θ}{2} x^{2} + x s i n θ + s i n^{2} θ & 1 + \frac{s i n 2 θ}{2} & 3 s i n^{2} θ \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

$I .$ $x cos θ + y sin θ = a$ , $x sin θ - y cos θ = b$	$a)$ $(x^{2} - y^{2})^{2} = 16 x y$
$I I .$ $x = sec θ + tan θ$ , $y = sec θ - tan θ$	$b)$ $x y = 1$
$I I I .$ $x sec θ + y tan θ = a$ , $x tan θ + y sec θ = b$	$c)$ $x^{2} - y^{2} = a^{2} - b^{2}$
$I V .$ $x = cot θ + cos θ$ , $y = cot θ - cos θ$	$d)$ $x^{2} + y^{2} = a^{2} + b^{2}$

x cos θ + y sin θ = 2

x sin θ - y cos θ = \sqrt{2}

x^{2} + y^{2} =

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