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Trigonometry
Pregunta

Simplifying a Trigonometric Expression In Exercise...

Simplifying a Trigonometric Expression In Exercises \(33 - 40\) , use the fundamental identities to simplify the expression. (There is more than one correct form of each answer.) 33. \(\tan \theta \csc \theta\) 

35. \(\sin \phi ( \csc \phi - \sin \phi )\) 

37. \(\sin \beta \tan \beta + \cos \beta\) 

39. \(\frac { 1 - \sin ^ { 2 } x } { \csc ^ { 2 } x - 1 }\) 

Answer

Simplify \( \sin ( x ) ( \csc ( x ) - \sin ( x ) ) : \cos ^ { 2 } ( x ) \) 

Steps 

\( \sin ( x ) ( \csc ( x ) - \sin ( x ) ) \) 

Express with sin, cos 

\( = 1 - \sin ^ { 2 } ( x ) \) 

Rewrite using trig identities 

\( = \cos ^ { 2 } ( x )\) 

Solución
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