what cos teta cant be 1/root2 (Question:327733.0)

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Chakradhar

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· 1 Months ago

what cos teta cant be 1/root2 (Question:327733.0)

7sin2θ+3cos2θ=4 3sin2θ+3cos2θ+4sin2θ=4 ⇒3(sin2θ+cos2θ)+(4sin2θ)=4 ⇒4-3=4sin2θ ⇒(sinθ=1/√2)....... so teta=45....

Question:

If $7 s i n^{2} θ + 3 c o s^{2} θ = 4$ then value of $c o s θ (0 < θ < 9 0^{0})$ is

Options:

$\frac{\sqrt{6}}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{\sqrt{2}}{2}$

$\frac{\sqrt{5}}{2}$

Solution:

$\begin{matrix} 7 s i n^{2} θ + 3 c o s^{2} θ = 4 \\ 3 s i n^{2} θ + 3 c o s^{2} θ + 4 s i n^{2} θ = 4 \\ \Rightarrow 3 (s i n^{2} θ + c o s^{2} θ) = 4 (1 - s i n^{2} θ) \\ \Rightarrow \frac{3}{4} = c o s^{2} θ \\ \Rightarrow (c o s θ = \frac{\sqrt{3}}{2}) \end{matrix}$

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what cos teta cant be 1/root2 (Question:327733.0)

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