Question

5. If coto - cosece = k then find the value of coseco + coto.
FOR BRAINLIEST OOOOOOOOOOOOOOOOOOOOKKKKK​

Answer 1

$\begin{gathered}\begin{gathered}\bf \: Given - \begin{cases} &\tt{cosec \theta \: - \: cot\theta \: = \: k } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To\:find - \begin{cases} &\sf{cosec\theta \: + cot\theta \: }  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

Given that

$\tt \longmapsto\:cosec\theta \: - cot\theta \: = k$

We know,

$\tt \longmapsto\: \pink{{cosec}^{2} \theta \: - {cot}^{2} \theta \: = 1}$

$\rm :\implies\:(cosec\theta \: - cot\theta \: )(cosec\theta \: + cot\theta \: ) = 1$

$\rm :\implies\:k(cosec\theta \: + cot\theta \: ) = 1$

$\rm :\implies\:\:\boxed{ \green{ \bf \:cosec\theta \: + cot\theta \: = \dfrac{1}{k} }}$

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