Which of the following is represented by cos2- - 2cos3- sin-sin4- - sin2- cos2- - 2sin3- cos- -

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Sin2A and Cos2A in Terms of tanA

Which of the ...

Question

Which of the following is represented by $\frac{c o s^{2} θ - 2 c o s^{3} θ s i n θ}{s i n^{4} θ + s i n^{2} θ c o s^{2} θ - 2 s i n^{3} θ c o s θ}$ ?

t a n^{2} θ

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c o t^{2} θ

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s i n^{2} θ - c o s^{2} θ

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1 - c o t^{2} θ

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Solution

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2 sin 3 θ cos θ - sin 4 θ - sin 2 θ

\frac{\cos^{4} θ + \cos^{2} θ \sin^{2} θ + \sin^{2} θ}{\cos^{2} θ + \cos^{2} θ \sin^{2} θ + \sin^{4} θ}

[\begin{matrix} cos 2 θ & - sin 2 θ sin 2 θ & cos 2 θ \end{matrix}]

(\frac{1}{\sec^{2} θ - \cos^{2} θ} + \frac{1}{{cosec}^{2} θ - \sin^{2} θ}) \sin^{2} θ \cos^{2} θ = \frac{1 - \sin^{2} θ \cos^{2} θ}{2 + \sin^{2} θ \cos^{2} θ}

(\frac{1}{\sec^{2} θ - \cos^{2} θ} + \frac{1}{{cosec}^{2} θ - \sin^{2} θ}) \sin^{2} θ \cos^{2} θ = \frac{1 - \sin^{2} θ \cos^{2} θ}{2 + \sin^{2} θ \cos^{2} θ}

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