Question

(Sec theta - Tan theta) =1-sin theta / 1+sin theta​

Answer 1

Step-by-step explanation:

Take LHS.

Let us square the LHS

So , (Sec θ -tan θ)²

We know [Sec θ=1/Cos θ] and [Tan θ=Sin θ/Cos θ]

(1/Cos θ - Sin θ/Cos θ)²

(1-Sin θ/Cos θ)²

(1-Sin θ)²/Cos² θ

[Splitting (1-Sin θ)² =(1-Sin θ) (1-Sin θ)]

[Cos² θ =1-Sin² θ]

So, (1-Sin θ) (1- Sin θ) / 1-Sin² θ

(1-Sin θ) (1-Sin θ) / (1-Sin θ) (1+Sin θ)

[1-Sin θ gets cancelled in both numerator and denominator]

So, (1-Sin θ)/ (1+Sin θ)

Hence proved........