IMPOSSIBLE trig identity- My son had this is a math contest but, i couldn't solve it Please give it a try :)

[David_Gomez]

Prove that the following identity is true:

I used online solvers but couldn't find a full solution
The provided equation is an identity but there are no steps available.

 

[Dr.Peterson]

What did you or he try in terms of thinking for yourselves (as opposed to looking up answers)? That would be much more helpful in order to help you both learn.

Here's how I started (and it did work out nicely):

Start with the LHS and express it in terms of sines only; then factor and simplify. You'll end up with something quite simple. Then do the same with the RHS. The result will be a demonstration that both are equal to the same thing, and therefore to one another.

 

[JeffM]

Prove that the following identity is true:
View attachment 15052
I used online solvers but couldn't find a full solution
The provided equation is an identity but there are no steps available.

Here is a hint to get you started: work with the sine function by using

[MATH]sin^2(x) + cos^2(x) = 1 \implies cos^2(x) = 1 - sin^2(x).[/MATH]
See where that takes you.

 

[David_Gomez]

Thank you, we had already tried with the Pythagorean identities but we couldn't find the right solution; although, we had missed a simple factorization, that was the thing that keep us stuck

 

[Dr.Peterson]

Excellent.

 

[Steven G]

Nice job!