Question

If 2.(cos²‎ (45°) + tan²‎ (60°)) - x(sin²‎ (45°) - tan²‎ (30°)) = 6, then find the value of x using trigonometric identities.

Answer 1

Plug in all of those cosine, tangent, and sine values... those are unit circle values (or if you know the "special" 30-60-90 and 45-45-90 triangles and SOHCAHTOA, you can use those). Then you'll just have a simple equation in x, solve for x.

Answer 2

I'll help you get started:

\(\Large 2(\cos²‎ (45°) + \tan²‎ (60°)) - x(\sin²‎ (45°) - \tan²‎ (30°)) = 6\\
\Large 2((\dfrac{1}{\sqrt{2}})^2 + \tan²‎ (60°)) - x(\sin²‎ (45°) - \tan²‎ (30°)) = 6\\
\Large 2(\dfrac{1}{2} + \tan²‎ (60°)) - x(\sin²‎ (45°) - \tan²‎ (30°)) = 6\)

That's the first term, now do that with the other function values.

Answer 3

I'm sorry, the complete questions says "Find the value of x using trigonometric identities". I somehow missed that part.

Answer 4

Hmmm.... ok..... well, one COULD argue that anytime you evaluate a trig function you are using trig identities ;) lol....

.... but it sounds like it's looking for something else, let me look at it for a minute....

Answer 5

I'm not seeing it. The only obvious application of an ID that I see is the cofunction ID lets you say that cos(45)=sin(45) and so their squares are also equal, so you can replace one of them with the other.... but I'm not sure that's much help.

@thomaster @skullpatrol any ideas...?

Answer 6

It's so trivial if we just plug in the function values.... lol

Answer 7

Thanks a lot for explaining! I'm sure there'll be a way to figure this out.