If 3-2-cos-sin-a-i b and a2-b2-a x-3- then x-

2 + cosθ + i sinθ/3 = 1/a + ib = a ib/a^2 + b^2 ⇒ 2 + cosθ = 3a/a^2 + b^2 sinθ = 3b/a^2 + b^2 sin^2 θ + cos^2 θ = 1 ⇒ a^2 + b^2 = 4a 3 = ax 3 ⇒ x = 4 ...

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Byju's Answer

Standard XII

Mathematics

Cos(A+B)Cos(A-B)

If 3/2+cosθ+s...

Question

If $\frac{3}{2 + c o s θ + i s i n θ} = a + i b$ and $a^{2} + b^{2} = a x - 3,$ then x =

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Solution

The correct option is A
4

$\frac{2 + c o s θ + i s i n θ}{3} = \frac{1}{a + i b} = \frac{a - i b}{a^{2} + b^{2}}$

$\Rightarrow 2 + c o s θ = \frac{3 a}{a^{2} + b^{2}} s i n θ = - \frac{3 b}{a^{2} + b^{2}}$

$s i n^{2} θ + c o s^{2} θ = 1 \Rightarrow a^{2} + b^{2} = 4 a - 3 = a x - 3$

$\Rightarrow$ x = 4

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If 32+cosθ+isinθ=a+ib and a2+b2=ax−3, then x =

The correct option is A 4 2+cosθ+isinθ3=1a+ib=a−iba2+b2 ⇒2+cosθ=3aa2+b2sinθ=−3ba2+b2 sin2θ+cos2θ=1⇒a2+b2=4a−3=ax−3 ⇒ x = 4

If $\frac{3}{2 + c o s θ + i s i n θ} = a + i b$ and $a^{2} + b^{2} = a x - 3,$ then x =