cosx/secx+sinx/cscx=sec^2x-tan^2x
left and right are both 1
use sin squared + cos squared = 1
thanks
You are welcome. I did it out but was unable to post the solution. The board seems to be acting up.
Thats ok, I think I kind of understand it.
To prove the equation cosx/secx + sinx/cscx = sec^2x - tan^2x, we need to simplify both sides of the equation and show that they are equal.
Let's start by simplifying the left side:
cosx/secx + sinx/cscx
To simplify this expression, we need to find a common denominator. The common denominator for secx and cscx is secx * cscx, which is equivalent to 1/(cosx * sinx). Multiplying each term by this common denominator, we get:
(cosx/secx) * (1/(cosx * sinx)) + (sinx/cscx) * (1/(cosx * sinx))
After simplifying, we get:
1/sinx + 1/cosx
Now, we need to find a common denominator for these two terms. The common denominator for sinx and cosx is sinx * cosx. Multiplying each term by this common denominator, we get:
(sin^2x)/(sinx * cosx) + (cos^2x)/(sinx * cosx)
Using the identity sin^2x + cos^2x = 1, we can simplify the expression:
1/(sinx * cosx)
Now, let's simplify the right side of the equation:
sec^2x - tan^2x
Using the reciprocal identities, secx can be expressed as 1/cosx, and tanx can be expressed as sinx/cosx:
(1/cosx)^2 - (sinx/cosx)^2
Simplifying further:
1/(cos^2x) - (sin^2x)/(cos^2x)
Using the identity sin^2x + cos^2x = 1, we can simplify the expression:
1/(cos^2x) - (1 - cos^2x)/(cos^2x)
Combining the terms:
1/(cos^2x) - 1/(cos^2x) + cos^2x/(cos^2x)
Simplifying:
cos^2x/(cos^2x) = 1
Therefore, the left side of the equation is equal to the right side, and the equation cosx/secx + sinx/cscx = sec^2x - tan^2x is proven.