# If sinθ =3, the Numerical Value of (secθ-tanθ)/(secθ+tanθ) is:

**Answer : (1) 1/4**

**Explanation:-
In the triangle-
**

**5Sinθ = 3**

Then, sinθ = 3/5 = AB/AC

Then, AB = 3 & AC = 5

BC = (5^2 – 3^2)^1/2

=( 25 – 9)^1/2

= (16)^1/2

BC = 4

Cosθ = 4/5 = BC/AC

Then, secθ = 1/cosθ

secθ = 1/(4/5)

secθ = 5/4

tanθ = sinθ/cosθ

Put the value of sinθ = 3/5 & cosθ = 4/5

Then, tanθ = (3/5)/(4/5)

= 3/4

(secθ-tanθ)/(secθ+tanθ) = (5/4 – 3/4)/(5/4 + 3/4)

= (2/4)/(8/4)

= (1/2)/2

= 1/4

Then, the value of (secθ-tanθ)/(secθ+tanθ) is 1/4.

Hence, the answer is (1) 1/4.

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