Trigonometric Identities

Write the trigonometric expression in terms of sine and cosine, and then simplify.

1. (a) \(\cos(t) \csc(t) \)   (b) \( 4 \cos(t) \tan (t)\)   (c) \( \dfrac{\sec(x)}{\csc(x)}\)   solution

2. (a) \(\sec(\theta) \cot(\theta) \)   (b) \(\cot^2(x)-\csc^2(x) \)   solution

B. Establish each identity.

1. (a)  \( \dfrac{\cot x}{\csc x}=  \cos x \)      (b)  \(\cos \theta \cdot \csc \theta  \cdot \tan \theta = 1 \)     (c)  \(\csc \theta \cdot \tan \theta = \sec \theta \)     solution

2.  \( \sec\theta - \sec\theta \sin^2\theta = \cos\theta\)  solution

3. \( (\sin \theta + \cos \theta)^2 + (\sin \theta - \cos \theta)^2 =2 \)  solution