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

1. 1/4
2. 1/2
3. 1/3
4. 1/5
Monis Rasool Professor Asked on 31st August 2015 in

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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.

Anurag Mishra Professor Answered on 31st August 2015.