Value of cos 2 20 o -cos 2 70 o sin 2 59 o -sin 2 31 o

The correct option is B 1 cos ^ 2 20 ^ o +sin ^ 2 20 ^ o #160; sin ^ 2 59 ^ o +cos ^ 2 59 ^ o #160; = 1 1 =1 ...

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AM,GM,HM Inequality

Value of co...

Question

Value of $\frac{{cos}^{2} 20^{o} + {cos}^{2} 70^{o}}{{sin}^{2} 59^{o} + {sin}^{2} 31^{o}}$

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\frac{1}{2}

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\frac{{s i n}^{2} 70^{o}}{{c o s}^{2} 20^{o}} + \frac{{c s c}^{2} 20^{o}}{{s e c}^{2} 70^{o}} - 2 c o s 70^{o} c o s e c 20^{o}

\frac{{sin}^{2} 20^{o} + {cos}^{4} 20^{o}}{{sin}^{4} 20^{o} + {cos}^{2} 20^{o}}

{sin}^{2} 65^{o} + {sin}^{2} 25^{o} + {cos}^{2} 35^{o} + {cos}^{2} 55^{o}

θ

θ = 0

\frac{π}{2}

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + {sin}^{2} θ & {cos}^{2} θ & 4 sin 4 θ {sin}^{2} θ & 1 + {cos}^{2} θ & 4 sin 4 θ {sin}^{2} θ & {cos}^{2} θ & 1 + 4 sin 4 θ \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

θ

θ = 0

θ = π / 2

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + s i n^{2} θ & c o s^{2} θ & 4 s i n 4 θ s i n^{2} θ & 1 + c o s^{2} θ & 4 s i n 4 θ s i n^{2} θ & c o s^{2} θ & 1 + 4 s i n 4 θ \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

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