Question

$\huge \bf \it \color{yellow}{if \: \cot( \theta) = \frac{7}{8} }$
$\small \bf \it \color{red}{ \underline{ \underline{then \: evaute \: the \: following}}}$

$\huge \bf \it \color{yellow}{ \frac{(1 - \sin \theta)(1 + \sin\theta)}{(1 - \cos\theta)(1 + \cos\theta) }}$
$<marquee bgcolor="aqua">$revelent answer will mark brillant and irrevelent will be reported​

Answer 1

$\rm \large \cot( \theta) = \frac{7}{8}$

Now,

$\rm \large \frac{(1 - sin \theta)(1 + sin \theta)}{(1 - cos \theta)(1 + cos \theta)} = \frac{ {(1})^{2} - {(sin \theta)}^{2} }{ {(1)}^{2} - {(cos \theta)}^{2} }$

$\rm \large = \frac{ 1- {(sin \theta)}^{2} }{ 1 - {(cos \theta)}^{2} }$

$\rm \large = \frac{ ({cos \theta})^{2} }{ {(sin \theta)}^{2} }$

$\rm \large = {( \frac{cos \theta}{sin \theta} )}^{2}$

$\rm = {(cot \theta)}^{2}$

$= { (\frac{7}{8} })^{2}$

$= \frac{49}{64}$

Hence, the required answer is 49/64.

Answer 2

Answer:

cot(θ)=87

Now,

\rm \large \frac{(1 - sin \theta)(1 + sin \theta)}{(1 - cos \theta)(1 + cos \theta)} = \frac{ {(1})^{2} - {(sin \theta)}^{2} }{ {(1)}^{2} - {(cos \theta)}^{2} }(1−cosθ)(1+cosθ)(1−sinθ)(1+sinθ)=(1)2−(cosθ)2(1)2−(sinθ)2

\rm \large = \frac{ 1- {(sin \theta)}^{2} }{ 1 - {(cos \theta)}^{2} }=1−(cosθ)21−(sinθ)2

\rm \large = \frac{ ({cos \theta})^{2} }{ {(sin \theta)}^{2} }=(sinθ)2(cosθ)2

\rm \large = {( \frac{cos \theta}{sin \theta} )}^{2}=(sinθcosθ)2

\rm = {(cot \theta)}^{2}=(cotθ)2

= { (\frac{7}{8} })^{2}=(87)2

= \frac{49}{64}=6449

Hence, the required answer is 49/64.