Question

$(1-{\cos }^2\theta )cose{c}^2\theta =1$

• A. True
• B. False

Answer 1

The correct option is A True

$(1-{\cos }^2\theta ){\csc }^2\theta$

$={\sin }^2\theta {\csc }^2\theta$ since $1-{\cos }^2\theta ={\sin }^2\theta$

$={\sin }^2\theta \times \frac{1}{{\sin }^2\theta }$ since ${\csc }^2\theta =\frac{1}{{\sin }^2\theta }$

$=1$

Hence the given statement is true.