# Trigo Identity applications

1. Sep 1, 2008

### ritwik06

1. The problem statement, all variables and given/known data
If $$\frac{(cos x)^{4}}{(cos y)^{2}}+\frac{(sin x)^{4}}{(sin y)^{2}}=1$$ prove that

$$\frac{(cos y)^{4}}{(cos x)^{2}}+\frac{(sin y)^{4}}{(sin x)^{2}}=1$$

3. The attempt at a solution
$$(cos x)^{4} (sin y)^{2}+(sin x)^{4} (cos y)^{2}=(sin y)^{2}-(sin y)^{4}$$

On simplification:
$$\frac{(sin y)^{4}}{(sin x)^{2}}=(sin y)^{2}+ (cos x)^{2} (sin y)^2 - (sin x)^{2}(cos y)^{2}$$

Similarly for cos
$$\frac{(cos y)^{4}}{(cos x)^{2}}=(cos y)^{2}+ (cos y)^{2} (sin x)^2 - (cos x)^{2}(sin y)^{2}$$

Adding the above gives the result.

But is their any simpler way?

2. Sep 1, 2008

### morphism

Am I missing something, because both your identities are identical?!

3. Sep 2, 2008

### ritwik06

There is nothing missing. Please check it out once again, they are indeed different.