Improve Your Math Fluency Series $\newline$ Instructions: Derive the indicated equation by combining trig identities (and, w) applicable, the definitions of secant, cosecant, and cotangent) together through substit nd applying algebra. There are no answers to these problems in the back of the ince the answer is instead given in the question). $\newline$ Use trig identities to show that $\cot ^{2} \theta+\csc ^{2} \theta=2 \csc ^{2} \theta-1$ .

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Algebra 2

Conjugate root theorems

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Q. Improve Your Math Fluency Series

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Instructions: Derive the indicated equation by combining trig identities (and, w) applicable, the definitions of secant, cosecant, and cotangent) together through substit nd applying algebra. There are no answers to these problems in the back of the ince the answer is instead given in the question).

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Use trig identities to show that

\cot ^{2} \theta+\csc ^{2} \theta=2 \csc ^{2} \theta-1

Recall identity: Recall the identity $\cot^2\theta = \csc^2\theta - 1$ .
Substitute in equation: Substitute $\cot^2\theta$ with $\csc^2\theta - 1$ in the given equation. $\newline$ So, $(\csc^2\theta - 1) + \csc^2\theta = 2\csc^2\theta - 1$ .
Combine like terms: Combine like terms on the left side of the equation. $\newline$ $2\csc^2\theta - 1 = 2\csc^2\theta - 1$ .