Question

(1+tanx+secx)(1+cotx-cosecx)

Answer 1

Answer:

Value of the given expression is 2.

Step-by-step explanation:

Given Expression,

( 1 + tan x + sec x )( 1 + cot x - cosec x )

To find: Value of the given expression.

Consider,

( 1 + tan x + sec x )( 1 + cot x - cosec x )

$=(1+\frac{sin\,x}{cos\,x}+\frac{1}{cos\,x})(1+\frac{cos\,x}{sin\,x}-\frac{1}{sin\,})$

$=(\frac{cos\,x+sin\,x+1}{cos\,x})(\frac{sin\,x+cos\,x-1}{sin\,x})$

$=(\frac{(cos\,x+sin\,x)+1}{cos\,x})(\frac{(cos\,x+sin\,x)-1}{sin\,x})$

$=\frac{(cos\,x+sin\,x)^2-1^2}{cos\,x\:sin\,x}$

$=\frac{cos^2\,x+sin^2\,x+2\:cos\,x\:sin\,x-1}{cos\,x\:sin\,x}$

$=\frac{1+2\:cos\,x\:sin\,x-1}{cos\,x\:sin\,x}$

$=\frac{2\:cos\,x\:sin\,x}{cos\,x\:sin\,x}$

$=2$

Therefore, Value of the given expression is 2.

Answer 2

Answer:

(sinx+coax)^2+(sinx-cosx)^2