Question

Simplify- (1-cosø) (1+cosø) × cosec2ø

Answer 1

Answer:

$\tan \theta$

Step-by-step explanation:

Given ,

$(1 - \cos\theta) (1 + \cos \theta) \times \ cosec2 \theta \\ \\ = ({1}^{2} - { \cos }^{2} \theta ) \cosec 2\theta \\ \\ = (1 - { \cos}^{2} 2\theta) \cosec 2\theta \\ \\ = { \sin }^{2} \theta \times \cosec2 \theta \\ \\ = { \sin }^{2} \theta \times \frac{1}{ \sin2 \theta } \\ \\ = { \sin }^{2} \theta \times \frac{1}{ \sin\theta \times \cos \theta} \\ \\ = \frac{ \sin \theta }{ \cos \theta } \\ \\ = \tan \theta$

Answer 2

$1 - \cos {}^{2} = \sin {}^{2}$

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

Answer is 1