Sure, I can help you with that!
First, let's break down the terms in the equation:
- sec beta: This is the reciprocal of the cosine of angle beta. In other words, sec beta = 1/cos beta.
- sin beta: This is the sine of angle beta.
- tan beta: This is the tangent of angle beta, which is equal to sin beta / cos beta.
Now, let's substitute these values into the equation:
sec beta * sin beta / tan beta = 1
(1/cos beta) * sin beta / (sin beta / cos beta) = 1
simplify by cancelling out the sin beta terms:
(1/cos beta) * 1 / (1 / cos beta) = 1
simplify further by multiplying by the reciprocal:
(cos beta / 1) * (cos beta / 1) = 1
cos^2 beta = 1
This is true because cosine squared of any angle is equal to one minus sine squared of that angle (cos^2 x + sin^2 x = 1). Therefore, the original equation sec beta * sin beta / tan beta = 1 is indeed true.