Question

sec x (1- sin x) (sec x + tan x) =1

prove..
class 11​

Answer 1

Answer:

Step-by-step explanation:

Given :

To prove :

sec x (1- sin x) (sec x + tan x) =1

Solution :

We know that,

$a^2 - b^2 = (a+b)(a-b)$  ...(i)

$sec x = \frac{1}{cosx}$,

$tan x = \frac{sinx}{cosx}$,

$sin^2x+cos^2x=1$

⇒ $cos^2x = 1-sin^2x$

Hence,

LHS = sec x (1- sin x) (sec x + tan x)

⇒ $\frac{1}{cosx} (1-sinx)(\frac{1}{cosx} + \frac{sinx}{cosx})$

⇒ $(\frac{1-sinx}{cosx}) \times (\frac{1+sinx}{cosx} )$

⇒ $\frac{1-sin^2x}{cos^2x}$  By (i) [here, a = 1 , b = sin x]

⇒ $\frac{cos^2x}{cos^2x} = 1$ = RHS

Hence, proved.