sec^2x/tanx -(tanx)
how to simplify
sec^2x/tanx -(tanx)
= (1/cos^2x)(cosx/sinx) - sinx/cosx
= 1/(sinxcosx) - sinx/cosx
= (1 - sin^2x)/(sinxcosx)
= cos^2x / (sinxcosx)
= cosx/sinx
= cot x
To simplify the expression (sec^2x / tanx) - (tanx), we can use trigonometric identities. Here's how to simplify this expression step by step:
Step 1: Rewrite sec^2x using the identity: sec^2x = 1 + tan^2x.
(1 + tan^2x) / tanx - tanx
Step 2: Simplify the numerator by expanding the squared term.
(1 + tan^2x) / tanx - tanx
Step 3: Combine the terms over a common denominator.
[(1 + tan^2x) - tan^2x] / tanx
Step 4: Simplify the numerator by canceling out the common term.
(1) / tanx
Step 5: Simplify further by using the reciprocal identity: tanx = 1/cotx.
(1) / (1/cotx)
Step 6: Multiply the numerator and the denominator by cotx to rationalize the denominator.
1 * cotx / 1
cotx
Therefore, the simplified expression is cotx.