Question

If Secx-tanx=3 then sinx =
1)2/3
2)2/5
3)1/3
4)4/5​

Answer 1

Option (4)

Step-by-step explanation:

Given :-

Sec x - Tan x = 3

To find :-

Find the value of Sin x ?

Solution :-

Given that :

Sec x - Tan x = 3 ------------(1)

We know that

Sec² x - Tan² x = 1

=> (Sec x + Tan x ) (Sec x - Tan x ) = 1

Since (a+b)(a-b) = a²-b²

Where, a = Sec x and b = Tan x

=>(Sec x + Tan x)(3) = 1

=> Sec x + Tan x = 1/3 -------(2)

On adding (1)&(2)

Sec x -Tan x = 3

Sec x + Tan x = 1/3

(+)

_______________

2 Sec x + 0 = 3+(1/3)

_______________

=> 2 Sec x = 3+(1/3)

=> 2 Sec x = (9+1)/3

=> 2 Sec x = 10/3

=> Sec x = (10/3)/2

=> Sec x = 10/(3×2)

=> Sec x = 10/6

=> Sec x = 5/3

=> 1 / Cos x = 5/3

=> Cos x = 3/5

On squaring both sides then

=> (Cos x)² = (3/5)²

=> Cos² x = 9/25

On Subtracting the above equation from 1 both sides then

=> 1 - Cos² x = 1 -(9/25)

=> 1 - Cos² x = (25-9)/25

=> 1- Cos² x = 16/25

=> Sin² x = 16/25

We know that

Sin² x + Cos² x = 1

=> Sin x = √(16/25)

=> Sin x = 4/5

Therefore, Sin x = 4/5

Answer:-

The value of Sin x for the given problem = 4/5

Used formulae:-

• (a+b)(a-b) = a²-b²
• Sec² x - Tan² x = 1
• Sin² x + Tan² x = 1
• Sec x = 1/Cosx