Question

(1-cosθ)(1+cosθ)(1+cot^2θ) =​

Answer 1

Step-by-step explanation:

please consider theta as @

(1-cos@)(1+cos@)(1+cot^2@)=(1-cos^2@)(cosec@) [ [1+cot^2@=cosec@]

=>sin@×cosec@=1

Answer 2

Step-by-step explanation:

Given :

$(1 - \cos \alpha )(1 + \cos\alpha ) (1 + { \cot }^{2} \alpha )$

=

$(1 - { \cos }^{2} \alpha )(1 + { \cot }^{ 2 } \alpha )$

=

${ \sin }^{2} \alpha \: \times \: {cosec}^{2} \alpha$

= 1

Note :--

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

$1 + { \cot }^{2} \alpha \: = {cosec}^{2} \alpha$

${cosec}^{2} \alpha \: = \frac{1}{ { \sin }^{2} \alpha }$