Trigonometric Identities - Higher Mathematics.

[c.carr]

Here's my question:

Given that "Sin (Theta + Alpha) = 0.6" and "Cos (Theta + Alpha) = 0.8", Show that:

"4 Tan(theta) + 4 Tan(alpha) + 3 Tan(theta) * Tan(alpha) = 3"

I cannot figure this out for the life of me, I've scribbled no end of drafts up onto paper and I cannot get anwhere with this

I've been shown that "Tan(theta) = Sin(theta) / Cos (theta)"

So assume that "Sin(theta + alpha) / Cos (theta + alpha) = Tan (theta + alpha)" but I'm still not getting anywhere, If anyone could provide me links to some decent websites with formula's or worked examples that are similar that would be really appreciated. Also, I was told that Compound Angles have something to do with this but I cannot make sense of where I can use it :/

Thanks in advance.

 

[stapel]

What identities have you been given?

 

[srmichael]

Here's my question:

Given that "Sin (Theta + Alpha) = 0.6" and "Cos (Theta + Alpha) = 0.8", Show that:

"4 Tan(theta) + 4 Tan(alpha) + 3 Tan(theta) * Tan(alpha) = 3"

I cannot figure this out for the life of me, I've scribbled no end of drafts up onto paper and I cannot get anwhere with this

I've been shown that "Tan(theta) = Sin(theta) / Cos (theta)"

So assume that "Sin(theta + alpha) / Cos (theta + alpha) = Tan (theta + alpha)" but I'm still not getting anywhere, If anyone could provide me links to some decent websites with formula's or worked examples that are similar that would be really appreciated. Also, I was told that Compound Angles have something to do with this but I cannot make sense of where I can use it :/

Thanks in advance.

Have you learned the sum and difference identities?

 

[Quaid]

I've been shown that Tan(theta) = Sin(theta) / Cos (theta)

So assume that Sin(theta + alpha) / Cos (theta + alpha) = Tan (theta + alpha)

You don't need to assume because the first identity above confirms the second. That is, θ+α is simply another angle. Identities hold true for all angles where both sides are defined.

If anyone could provide me links to some decent websites with [identities]

http://www.sosmath.com/trig/Trig5/trig5/trig5.html


Did you use the identity and givens, yet, to determine the numerical value of tan(θ+α) ?

Hopefully, you're allowed to use the tangent identity for a sum of angles. Then, you could replace tan(θ+α) with its value, and rearrange the resulting equation to the desired form, using algebra.

:smile: