Eight Fundamental Identities
Sec thada - Cos thada
How do I do this?
There is no equal sign so no identity.
sec t = 1/cos t
by definition if that helps
sec ( theta ) = 1 / cos ( theta )
sec ( theta ) - cos( theta ) =
[ 1 / cos ( theta ) ] - cos ( theta ) =
[ 1 - cos ^ 2 ( theta )] / cos ( theta ) =
sin ^ 2 ( theta) / cos ( theta ) =
sin ( theta ) * sin ( theta ) / cos ( theta ) =
[ sin ( theta ) / cos ( theta ) ] * sin ( theta ) =
tan ( theta ) * sin ( theta )
To solve the expression "sec theta minus cos theta," we can use the fundamental identities of trigonometry. Let's break it down step-by-step:
1. Start with the expression: sec(theta) - cos(theta).
2. Recall the definition of secant (sec): sec(theta) = 1/cos(theta).
3. Substitute the definition of sec(theta) in the expression: 1/cos(theta) - cos(theta).
4. To combine the two terms with the common denominator, we need to find a common denominator. Multiply the first term (1/cos(theta)) by (cos(theta)/cos(theta)) to get: (cos(theta)/cos(theta)) - cos(theta).
5. Simplify the expression: cos(theta)/cos(theta) - cos(theta).
6. Combine the fractions with the common denominator: (cos(theta) - cos(theta))/cos(theta).
7. Since the numerator (cos(theta) - cos(theta)) is equal to zero, the expression simplifies to: 0/cos(theta), which is always equal to zero.
Therefore, sec(theta) - cos(theta) is equal to 0.