Perform the indicated operation and simplify the result COSs

Perform the indicated operation and simplify the result. COSsinz sec csc z Select the expression that completes the identity + CSc T Ocot+ tan a Otan2sec2 Ocsc +cot z csccotz sectan2 r

Solution

1) cosx/secx + sinx/cscx

we know secx = 1/cosx and cscx = 1/sinx

So,cosx/secx + sinx/cscx = cosx*(cosx) + sinx*(sinx) = cos^2x +sin^2x = 1

we know the identity : 1+cot^2x = csc^2x ----> 1 = csc^2x -cot^2x

So, cos^2x +sin^2x = 1 = csc^2x -cot^2x

Option :csc^2x -cot^2x