Question

if secx=√2. and 3π<x<2π,find the value of 1+tanx+cosecx/1+cotx-cosecx​

Answer 1

Hii..

secx=√2

x=45 degree

1+1+√2/1+1-√2

2+√2/2-√2

Answer 2

Answer:

-1

Step-by-step explanation:

From the question we know that x is lying in 4th quadrant..since 3π/2 < x < 2π where π=180 degree

we have sec x = √2..therefore..cos = 1/√2

Form formula-> sin²x = 1 - cos² x

we have_sin x = - 1/√2 ( minus because all value of trigonometry function are negative in forth quadrant except cos and sec )

Therefore cosec x = -√2 ( cosec x = 1/sinx )

now, tan x = -1 ( tan x = sin x / cos x)

and cot x = -1 too ( cot x = 1/tan x )

To find value of,

1 + tan x + cosec x

÷

1 + cot x - coesc x

Solution:-

= 1 - 1 - √2

÷

1 - 1- ( - √2)

= - √2

÷

√2

= -1 ( Answer )