Let's solve this fun trigonometric fun math problem!
1.) SEC²X-1/SIN²X
Again, you meant "simplify" ...
SEC²X-1/SIN²X
= sec^2 x - csc^2 x
= (tan^2x + 1) - (1 + cot^2x)
= tan^2x - cot^2x
To solve this trigonometric math problem, we will simplify the expression SEC²X - 1/SIN²X.
Step 1: Expand the expressions SEC²X and SIN²X.
SEC²X = (1/COSX)²
SIN²X = SIN²X
Step 2: Substitute the expanded expressions.
(1/COSX)² - 1/SIN²X
Step 3: Find the common denominator.
The common denominator is COS²X * SIN²X.
(1/COSX)² * SIN²X/COS²X - 1/COS²X
Step 4: Simplify the expression.
SIN²X/COS²X * SIN²X/COS²X - 1/COS²X
Step 5: Combine like terms.
(SIN⁴X - 1)/COS²X
So the simplified expression for SEC²X - 1/SIN²X is (SIN⁴X - 1)/COS²X.