do you know some trigonometric identities?

Geometry Level pending

Which of the following is equivalent to csc ⁡ 2 x ( − cos ⁡ 2 x + 1 ) \csc^2 x(-\cos^2 x + 1) ?

0 0 1 1 tan ⁡ x \tan x cos ⁡ x \cos x sin ⁡ x \sin x

Marvin Kalngan by Marvin Kalngan , 38, Philippines

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2 solutions

Mahdi Raza
Jun 3, 2020

\[\begin{align} \bigg(\csc^2{x}\bigg) &\cdot \bigg( 1 - \cos^2{x}\bigg) \\ \bigg( \dfrac{1}{\sin^2{x}} \bigg) &\cdot \big( \sin^2{x}\big) \\ &\boxed{1}

\end{align}\]

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Vilakshan Gupta
Jun 3, 2020

1 − cos ⁡ 2 x = sin ⁡ 2 x = 1 csc ⁡ 2 x 1-\cos^2 x =\sin^2 x= \dfrac{1}{\csc^2x} , hence answer is 1 \boxed{1} .

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