Question

If Cosec theta +Cot theta =3,then Cos theta =​

Answer 1

Answer:

$\huge \red { \ \cosθ = \frac{4}{5} }$

Step-by-step explanation:

$\cscθ + \cotθ = 3 \: \: ...(given)$

$\cotθ = 3 - \cscθ$

Squaring both sides,

$\cot^{2} θ = {(3 - \cscθ) }^{2}$

$\cot^{2}θ = 9 - 6 \cscθ + { \csc }^{2} θ$

$\cot^{2} θ - \csc^{2} θ = 9 - 6 \cscθ$

$- 1 = 9 - 6 \cscθ$

$6 \cscθ = 10$

$\cscθ = \frac{5}{3}$

$\sinθ= \frac{3}{5}$

$∴ \cosθ = \frac{4}{5}$

Answer 2

Given : Cosecθ + Cotθ  = 3

To Find : cosθ

Solution:

Cosecθ + Cotθ  = 3

=> 1/Sinθ + Cosθ/Sinθ  = 3

=> 1 + Cosθ  = 3Sinθ

=> 2Cos²(θ/2) = 6Sin(θ/2)Cos(θ/2)

=> Cos(θ/2)(Cos(θ/2) - 3Sin(θ/2)) = 0

=> Cos(θ/2) = 0   or tan(θ/2) = 1/3

Cosθ = 2Cos²(θ/2) - 1  

=  - 1

not possible as Cotθ not defined  for Cosθ  = -1

tan(θ/2) = 1/3

Cos θ = ( 1 - tan²(θ/2))/(1 + tan²(θ/2))

= (  1-  1/9)/(1 + 1/9)

= 8/10

= 4/5

Cosθ  = 4/5

Learn More:

(1-Tan)^2+(1-Cot)^2=(Sec-Cosec)^2 Prove - Brainly.in

https://brainly.in/question/11114886