A) cos2θ =cos^ 2 θ sin^ 2 θ =( cosθ +sinθ nbsp;) ( cosθ sinθ nbsp;) =xy B) sin2θ =1 ( cosθ sinθ nbsp;) ^ 2 =1 y^ 2 =x^ 2 1 C) cotθ = co ...

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Trigonometric Ratios of Allied Angles

cosθ+sinθ=x, ...

Question

$c o s θ + s i n θ = x, c o s θ - s i n θ = y$

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Solution

A) $c o s 2 θ = c o s^{2} θ - s i n^{2} θ = (c o s θ + s i n θ) (c o s θ - s i n θ) = x y$
B) $s i n 2 θ = 1 - {(c o s θ - s i n θ)}^{2} = 1 - y^{2} = x^{2} - 1$
C) $c o t θ = \frac{c o s θ}{s i n θ} = \frac{2 c o s θ}{2 s i n θ} = \frac{x + y}{x - y}$
D) $t a n 2 θ = \frac{s i n 2 θ}{c o s 2 θ} = \frac{x^{2} - 1}{x y}$

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