Question

If sin theta=a/b, find sec theta + tan theta in terms of a and b

Answer 1

The answer is given below :

sinθ = a/b

So, secθ = b/√(b² - a²)

and

tanθ = a/√(b² - a²)

Now,

secθ + tanθ

= b/√(b² - a²) + a/√(b² - a²)

= (b + a)/√(b² - a²)

Thank you for your question.

Answer 2

In terms of a and b, sec(θ) + tan(θ) = $(1 + a/b) / \sqrt(1 - (a/b)^2)$

Recall that the trigonometric functions are related as follows:

$sec(\theta) = 1/cos(\theta)$

$tan(\theta) = sin(\theta)/cos(\theta)$

Given sin(θ) = a/b, we can find cos(θ) as follows:

$cos^2(\theta) = 1 - sin^2(\theta) = 1 - (a/b)^2$

$cos(\theta) = \sqrt(1 - (a/b)^2)$

Then,

$sec(\theta) = 1/cos(\theta) = 1/\sqrt(1 - (a/b)^2)$

$tan(\theta) = sin(\theta)/cos(\theta) = a/b / \sqrt(1 - (a/b)^2)$

So,

$sec(\theta) + tan(\theta) = 1/\sqrt(1 - (a/b)^2) + a/b / \sqrt(1 - (a/b)^2)$

= $(1 + a/b) / \sqrt(1 - (a/b)^2)$

• Secant and tangent are trigonometric functions that are defined in terms of the sides of a right triangle.

• The secant of an angle is equal to the ratio of the hypotenuse to the adjacent side, while the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

• By using the definition of secant and tangent, we can find the value of sec theta + tan theta in terms of a and b.

• If sin theta = a/b, then we know that a is the opposite side and b is the hypotenuse of a right triangle.

Learn more about similar question visit:

brainly.in/question/36050112

brainly.in/question/40051804

#SPJ3