Question

plss give proper explanation​

Answer 1

Step-by-step explanation:

1/1-cosa÷1+/1cousa

answer=1casa

answer=1casa

2casa

Answer 2

$\green{\large\underline{\sf{Given \:Question - }}}$

The expression

$\rm :\longmapsto\: \sqrt{\dfrac{1 - cos \alpha }{1 + cos\alpha } } + \sqrt{\dfrac{1 + cos\alpha }{1 - cos\alpha } } =$

$\purple{\large\underline{\sf{Solution-}}}$

The given expression is

$\rm :\longmapsto\: \sqrt{\dfrac{1 - cos \alpha }{1 + cos\alpha } } + \sqrt{\dfrac{1 + cos\alpha }{1 - cos\alpha } }$

can be rewritten as

$\rm \:  =  \: \dfrac{ \sqrt{1 - cos\alpha } }{ \sqrt{1 + cos\alpha } } + \dfrac{ \sqrt{1 + cos\alpha } }{ \sqrt{1 - cos\alpha } }$

On taking LCM we get,

$\rm \:  =  \: \dfrac{ {\bigg[ \: \sqrt{1 - cos\alpha \: }\bigg] }^{2} + {\bigg[ \sqrt{1 + cos\alpha }\bigg] }^{2} }{ \sqrt{1 + cos\alpha } \: \sqrt{1 - cos\alpha } }$

$\rm \:  =  \: \dfrac{1 - cos\alpha + 1 + cos\alpha }{ \sqrt{(1 + cos\alpha )(1 - cos\alpha )} }$

We know,

$\green{ \boxed{ \sf{ \:(x + y)(x - y) = {x}^{2} - {y}^{2}}}}$

So, using this identity, we get

$\rm \:  =  \: \dfrac{2}{ \sqrt{1 - {cos}^{2}\alpha } }$

We know,

$\red{ \boxed{ \sf{ \: {sin}^{2}x + {cos}^{2}x = 1}}}$

$\rm \:  =  \: \dfrac{2}{ \sqrt{{sin}^{2}\alpha } }$

$\rm \:  =  \: \dfrac{2}{sin \alpha }$

$\rm \:  =  \: 2 \: cosec\alpha$

Hence,

$\red{\rm :\longmapsto\:\red{ \boxed{ \sf{ \: \sqrt{\dfrac{1 - cos \alpha }{1 + cos\alpha } } + \sqrt{\dfrac{1 + cos\alpha }{1 - cos\alpha } } = 2 \: cosec\alpha }}}}$

Additional Information:-

Relationship between sides and T ratios

sin θ = Opposite Side/Hypotenuse

cos θ = Adjacent Side/Hypotenuse

tan θ = Opposite Side/Adjacent Side

sec θ = Hypotenuse/Adjacent Side

cosec θ = Hypotenuse/Opposite Side

cot θ = Adjacent Side/Opposite Side

Reciprocal Identities

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ

Co-function Identities

sin (90°−x) = cos x

cos (90°−x) = sin x

tan (90°−x) = cot x

cot (90°−x) = tan x

sec (90°−x) = cosec x

cosec (90°−x) = sec x

Fundamental Trigonometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

cosec²θ - cot²θ = 1