Hello I am having trouble with proving this:
sinA/secA+secA/cscA = tan(A)(2-sin^2(A))
So far I've gotten
SinA/(1/cosA) + (1/cosA)/(1/sinA)
SinACosA + sinA/cosA
I am stuck here, not even sure if multiplying by the reciprocal was the right step..
on right
tan(A)(2-sin^2(A))
(sinA/cosA) (1 + cos^2A) because s^2+c^2 = 1
sinA / cosA + sinAcosA
looks like what you had on the left :)
Let's continue from where you left off.
You have reached the point: sinA/cosA + sinA/cosA
To simplify this expression, we can first find a common denominator for both terms. The common denominator would be cosA * cosA, which is cos²(A).
So, the expression becomes: (sinA * cosA + sinA * cosA) / cos²(A)
Now, let's simplify the numerator: sinA * cosA + sinA * cosA is equivalent to 2 * sinA * cosA (since the terms are the same)
The expression becomes: 2 * sinA * cosA / cos²(A)
Next, we can cancel out a factor of cosA from both the numerator and the denominator.
The expression simplifies to: 2 * sinA / cosA
And since sinA / cosA is equal to tanA, the expression can be further simplified to: 2 * tanA
Therefore, the final proof is: sinA/secA + secA/cscA = tan(A)(2-sin²(A))
Note: When proving an equation, it is important to start with one side of the equation and use algebraic manipulations to eventually reach the other side. In this case, you started with the left side and simplified it to match the right side of the equation.