express this in sinx
(1/ cscx + cotx )+ (1/cscx- cotx)
i got 2sinx is that right??
and B)
express in cosx
problem: is 1 + cotx/cscx - sin^2x
i get to the step of 1 + cos-sin^2x and im stuck..help!
(1/cscx + cotx) + (1/cscx - cotx) =
(sinx + cosx/sinx) + (sinx - cosx/sinx) =
2sinx
You are correct on that one!
Note: 1 - sin^2x = cos^2x
1 + cotx/cscx - sin^2x =
1 + cosx - sin^2x =
cos^2x + cosx
...or...
cosx (cosx + 1)
I hope this helps.
somebody posted the same question before, but they had it as
1/(cscx+cotx) + 1/(cscx - cotx)
this would reduce to 2csc x
which in terms of sinx would be 2/sinx
csc2x + 1 = 0
To express the expression (1/cscx + cotx) + (1/cscx - cotx) in terms of sinx, we can simplify it step by step:
Step 1: Convert cscx and cotx to sine and cosine:
(1/sinx + cosx/sinx) + (1/sinx - cosx/sinx)
Step 2: Combine the terms with a common denominator:
[(1 + cosx) + (1 - cosx)]/sinx
Step 3: Simplify the numerator:
[1 + cosx + 1 - cosx]/sinx
Step 4: Combine like terms:
2/sinx
So, the expression (1/cscx + cotx) + (1/cscx - cotx) simplifies to 2/sinx.
For the second part:
To express the expression 1 + cotx/cscx - sin^2x in terms of cosx, we can simplify it step by step:
Step 1: Convert cotx and cscx to sine and cosine:
1 + (cosx/sinx)/(1/sinx) - sin^2x
Step 2: Simplify the division:
1 + (cosx/sinx) * sinx - sin^2x
Step 3: Simplify the product:
1 + cosx - sin^2x
Step 4: Use the identity 1 - sin^2x = cos^2x:
cos^2x + cosx
or alternatively,
cosx * (cosx + 1)
So, the expression 1 + cotx/cscx - sin^2x simplifies to cos^2x + cosx, or cosx * (cosx + 1).
I hope this clarifies the process for you.