Pre-Calc/Trig Unit 3: Analytic Trig and Applications/5.2 Verifying Trig Identities Perform the indicated operations and simplify the result.tan θ(cot θ - cos θ) Perform the indicated operations and simplify the result.

tan θ(cot θ - cos θ)

]]> 1.0000000 0.3333333 0 true true abc 1

]]> Incorrect.  Distribute, then change to "sin" and "cos" before simplifying. 

]]> - sec²θ

]]> Incorrect.  Distribute, then change to "sin" and "cos" before simplifying. 

]]> 0

]]> Incorrect.  Distribute, then change to "sin" and "cos" before simplifying. 

]]> 1 - sin θ

]]> Correct. 

]]> Simplify the expression.sin θ cos θ sec θ csc θ Simplify the expression.

sin θ cos θ sec θ csc θ

]]> 1.0000000 0.3333333 0 true true abc sec²θ

]]> Incorrect.  Change to "sin" and "cos"

]]> csc²θ

]]> Incorrect.  Change to "sin" and "cos"

]]> 1

]]> Correct

]]> tan²θ

]]> Incorrect.  Change to "sin" and "cos"

]]> Simplify the expression.sin2 x(cot2 x + 1) Simplify the expression.

sin² x(cot² x + 1)

]]> 1.0000000 0.3333333 0 true true abc cos² x + 1

]]> Incorrect.  Substitute something in for (cot² x + 1)

]]> tan² x

]]> Incorrect.  Substitute something in for (cot² x + 1)

]]> 1

]]> Correct

]]> -1

]]> Incorrect.  Substitute something in for (cot² x + 1)

]]> Solve the problem.A wooden block sitting at rest on a flat, level board will ... Solve the problem.

A wooden block sitting at rest on a flat, level board will just begin to slide when the board is tilted up to a critical angle of inclination, θ_s . An experiment that determines this critical angle can be used to find the coefficient of static friction, μ_s , for the block on the board by using the relation   Rewrite this relation using a quotient identity.]]> 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 1.0000000 0.3333333 0 true true abc s = tan θ_s]]> Correct s = tan² θ_s]]> Incorrect s = cot θ_s]]> Incorrect s = sec θ_s]]> Incorrect Use the fundamental identities to simplify the expression. Use the fundamental identities to simplify the expression.

]]> 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 1.0000000 0.3333333 0 true true abc 1

]]> Incorrect.  Change all to "sin" and "cos" before simplifying.

]]> cot²θ

]]> Correct

]]> csc²θ

]]> Incorrect.  Change all to "sin" and "cos" before simplifying.

]]> sec²θ

]]> Incorrect.  Change all to "sin" and "cos" before simplifying.

]]> Use the fundamental identities to simplify the expression.tan2θ csc2θ Use the fundamental identities to simplify the expression.

tan²θ csc²θ

]]> 1.0000000 0.3333333 0 true true abc sin θ

]]> Incorrect.  Change all to "sin" and "cos" before simplifying.

]]> sec²θ

]]> Correct

]]> cos³θ

]]> Incorrect.  Change all to "sin" and "cos" before simplifying.

]]> tan²θ

]]> Incorrect.  Change all to "sin" and "cos" before simplifying.

]]>