Question

Prove (1+ sec θ)/ sec θ = (1+ cos θ)​

Answer 1

$\large\red{ \rm{Solution}}$

To Prove : (1+secθ)/secθ = (1+ cos θ)

Take L.H.S first,

$\sf \dfrac{1 + \sec\theta}{ \sec \theta}$

$\sf \dfrac{1}{ \sec \theta} + \dfrac{\sec \theta }{\sec \theta}$

'sec θ' will get cancelled out also,

1/secθ = cosθ

$\sf \cos \theta \: + 1$

or, 1 + cos θ ; L.H.S = R.H.S

Hence Proved

Answer 2

Answer:

it is proved that : (1+ sec θ)/ sec θ = (1+ cos θ)​

Step-by-step explanation:

given that :

we have to prove  (1+ sec θ)/ sec θ = (1+ cos θ)​

firstly , consider :

left side of given equation:

(1+ sec θ)/ sec θ

sec θ can be written as (1/cos θ)

substitute sec θ value in   (1+ sec θ)/ sec θ ;

= ( 1 + (1/cos θ) ) / (1/cos θ)

=[(cosθ+1)/cosθ] /  (1/cos θ)

=(cos  θ + 1)(cos θ/cos θ)

= cos θ + 1

we have RHS = (1+ cos θ)​

hence LHS = RHS

it is proved that : (1+ sec θ)/ sec θ = (1+ cos θ)​