Question

If sec teta minus tan teta is equal to one over four, find sec teta plus tan teta. ​

Answer 1

To find sec θ + tan θ, square both sides of sec θ - tan θ = 1/4 to get sec^2 θ - 2sec θ tan θ + tan^2 θ = 1/16. Simplify the equation and divide by sec θ - tan θ to find sec θ + tan θ = 15/4.the correct answer sec θ + tan θ = 15/4

Step-by-step explanation:

To find the value of sec θ + tan θ when given that sec θ - tan θ = 1/4, we can use the trigonometric identity:
sec θ^2 - tan θ^2 = 1

Since we're given that sec θ - tan θ = 1/4, we can square both sides to obtain:
(sec θ - tan θ)^2 = (1/4)^2

Expanding and simplifying the equation will give us:
sec^2 θ - 2sec θ tan θ + tan^2 θ = 1/16

Now, using the identity mentioned earlier, we can substitute the value of sec^2 θ - tan^2 θ with 1:

1 - 2sec θ tan θ = 1/16

After simplifying, we get:
2sec θ tan θ = 1 - 1/16
2sec θ tan θ = 15/16

Finally, to find the value of sec θ + tan θ, we can divide both sides of the equation by sec θ - tan θ:

2sec θ tan θ / (sec θ - tan θ) = (15/16) / (1/4)
2sec θ tan θ = 15/4

Therefore, sec θ + tan θ = 15/4.