How to verify the identity: (1-2cos^2(x))/(sin(x)cos(x))?
How does one verify 1−2cos2xsinxcosx=tanx−cotx using basic trig identities such as the Quotient Identities, the Reciprocal Identites, and the Pythagorean Identities?
How does one verify
3 Answers
Explanation:
Please look at the Explanation area for this is a "how" question.
Explanation:
The first step to this problem is to use a Pythagorean Identity:
But we only want to replace one of the
And then complete the substitution:
Next, distribute the negative and simplify:
Now we can split this fraction into two:
Simplify:
Apply the quotient identities:
And you reach:
Explanation:
using the trigonometric identities
∙xtanx=sinxcosx and cotx=cosxsinx
.
consider the right side
tanx−cotx
=sinxcosx−cosxsinx
=sin2x−cos2xsinxcosx
=1−cos2x−cos2xsinxcosx
=1−2cos2xsinxcosx= left side ⇒ verified