Determine: (\sec^2 \theta - 1)(\cosec^2 \theta - 1)

Anonymous
0
Step 1: Take the given question
(\sec^2 \theta - 1)(\cosec^2 \theta - 1)
Step 2: Find the suitable trigonometric identities to simplify the equation
NOTE: \sec^2 \theta - 1 = \tan \theta
\cosec^2 \theta - 1 = \cot \theta
Step 3: Substitute the trigonometric identities in the given equation
EXAMPLE: = (\sec^2 - 1)(\cosec^2 - 1)
= \tan \theta \cot \theta
= \tan\theta\ \cdot\frac{1}{\tan\theta} [since. \cot \theta = \frac{1}{\tan \theta}
= 1