Question

example 3: simplifying a trigonometric expression
example: simplify the trig expression
\\( \frac { \sin ^ { 2 } ( x ) - \tan ^ { 2 } ( x ) } { \tan ^ { 2 } ( x ) \sin ^ { 2 } ( x ) } \\)
\\( \frac { a + b } { c } = \frac { a } { c } + \frac { b } { c } \\)
\\( \csc \theta = \frac { 1 } { \sin \theta } \quad \sec \theta = \frac { 1 } { \cos \theta } \quad \cot \theta = \frac { 1 } { \tan \theta } \\)
\\( \tan \theta = \frac { \sin \theta } { \cos \theta } \quad \cot \theta = \frac { \cos \theta } { \sin \theta } \\)
simplify and write the trigonometric expression in terms of sine and cosine:
\\( \tan ^ { 2 } x - \sec ^ { 2 } x = \\)
question help: worked example 1

Explanation:

Step1: Use the trigonometric identity

We know the identity \(1 + \tan^{2}\theta=\sec^{2}\theta\), which can be rewritten as \(\tan^{2}\theta-\sec^{2}\theta=- 1\)

Answer:

\(-1\)