Question

If sec theta + tan theta = 1.5 and sec theta =a, tan theta = b, then the value of (a, b)is​

Answer 1

Given: secθ + tanθ = 1.5 and secθ = a, tanθ = b

To find: the value of (a, b)

Solution:

• We know that, sec²θ - tan²θ = 1

• or, (secθ + tanθ) (secθ - tanθ) = 1

• or, secθ - tanθ = 1/1.5, since secθ + tanθ = 1.5

• or, secθ - tanθ = 2/3

Using secθ = a and tanθ = b, we get

a + b = 3/2

a - b = 2/3

Adding the above equations, we get

2a = 3/2 + 2/3

or, 2a = (9 + 4)/6

or, 2a = 13/6

or, a = 13/12

We have: a + b = 3/2

or, 13/12 + b = 3/2

or, b = 3/2 - 13/12

or, b = 18/12 - 13/12

or, b = 5/12

Answer: (a, b) is (13/12, 5/12).

Answer 2

Answer:

Value of a, b = 13/12 , 5/12