Question

Verify the identity. \(\sin x + \sin x \cot^2 x = \csc x\) To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step. \(\sin x + \sin x \cot^2 x\) \(= \sin x \left(\boxed{\qquad}\right)\) (Do not simplify.) \(= \sin x \left(\boxed{\qquad}\right)\) Factor out the greatest common factor, \(\sin x\). Apply a reciprocal identity. \(= \boxed{\qquad}\) (Do not simplify.) Apply the appropriate even \( - \) odd identity. \(= \csc x\) Separate the quotient into two terms.

          Verify the identity.
\(\sin x + \sin x \cot^2 x = \csc x\)
To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the
correct transformations and transform the expression at each step.
\(\sin x + \sin x \cot^2 x\)
\(= \sin x \left(\boxed{\qquad}\right)\)
(Do not simplify.)
\(= \sin x \left(\boxed{\qquad}\right)\)
Factor out the greatest common factor, \(\sin x\).
Apply a reciprocal identity.
\(= \boxed{\qquad}\)
(Do not simplify.)
Apply the appropriate even \( - \) odd identity.
\(= \csc x\)
Separate the quotient into two terms.

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Verify the identity.
sin x + sin x cot^2 x = csc x
To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the
correct transformations and transform the expression at each step.
sin x + sin x cot^2 x
= sin x ( )
(Do not simplify.)
= sin x ( )
Factor out the greatest common factor, sin x.
Apply a reciprocal identity.
=
(Do not simplify.)
Apply the appropriate even - odd identity.
= csc x
Separate the quotient into two terms.

Added by Nicole V.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Kathleen Carty

04/16/2023

Step 1

Step 1: Start with the left side of the equation: sin^2(x) cot^2(x) + sin^2(x) Show more…

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Question content area top Part 1 Verify the identity. sine squared x cotangent squared x plus sine squared x equals 1 Question content area bottom Part 1 To verify that an equation is an identity, start with the more complicated side and transform the side of the equation into the other side by a sequence of steps, each of which produces an identity. sine squared x cotangent squared x plus sine squared x Begin with left side equals enter your response here plus sine squared x Verify the identity sinx + sinx cot^2 x = cscx To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step sinx + sinx cotx = sinx (Do not simplify.) = sinx Factor out the greatest common factor, sin x Apply a reciprocal identity Apply the appropriate even-odd identity (Do not simplify.) Separate the quotient into two terms = cscx

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