tan(to the second power) s sin(to second power)=tan(to second power + cos(second power) s - 1...I need the steps on how to get it to equal...problem looks like tan2 s sin2 s=tan2 s + cos2 s - 1...thanks if you can figure it out
To solve the equation tan^2(s) * sin^2(s) = tan^2(s) + cos^2(s) - 1, we can break it down step by step:
Step 1: Recall the Pythagorean identity for trigonometric functions: sin^2(x) + cos^2(x) = 1. We can rewrite cos^2(s) as 1 - sin^2(s).
Step 2: Replace cos^2(s) with 1 - sin^2(s) in the equation: tan^2(s) * sin^2(s) = tan^2(s) + (1 - sin^2(s)) - 1.
Step 3: Simplify both sides of the equation:
- On the left side, we have tan^2(s) * sin^2(s) which can be expanded as (tan(s) * sin(s))^2.
- On the right side, we have tan^2(s) + 1 - sin^2(s) - 1. Combining like terms, we get: tan^2(s) - sin^2(s) + 1.
Step 4: Replace tan^2(s) - sin^2(s) with tan^2(s) - sin^2(s) = tan^2(s) - sin^2(s). Now the equation becomes:
(tan(s) * sin(s))^2 = tan^2(s) - sin^2(s) + 1.
So, the equation tan^2(s) * sin^2(s) = tan^2(s) + cos^2(s) - 1 simplifies to:
(tan(s) * sin(s))^2 = tan^2(s) - sin^2(s) + 1.
This is the simplified form of the given equation.