If tanθ+secθ=2, then the value of tan θ is

(a) 2/3
(b) 3/5
(c) 4/5
(d) ¾

Anurag Mishra Professor Asked on 26th March 2016 in Maths.
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1 Answer(s)

Answer: (d) 3/4 

Solution:-
tanθ + secθ = 2   ………………… (1)

As we know that, sec²θ – tan²θ = 1
Then, (secθ – tanθ) (secθ + tanθ) = 1

From equation (1),
(secθ – tanθ) (2) = 1
secθ – tanθ = 1/2  …………….. (2)

Equation (2) subtract from equation (1),
(tanθ + secθ) – (secθ – tanθ) = 2-1/2
tanθ + secθ – secθ + tanθ = 3/2
2 tanθ = 3/2
tanθ = 3/4

Then, the value of tanθ is 3/4.

Hence, the correct answer is option (d) 3/4.

 

Anurag Mishra Professor Answered on 27th March 2016.
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