Paul Q. answered 04/01/20
Experienced in Math, Physics, Stat, Programming, & Meteorology
Alanna M.
asked 04/01/20prove the identity above
Paul Q. answered 04/01/20
Experienced in Math, Physics, Stat, Programming, & Meteorology
Lois C. answered 04/01/20
Knowledgeable, experienced tutor specializing in secondary mathematics
This identity can be proven by working only the left side of the equation. We begin by using the quotient identity for cotangent, allowing us to replace the cot2 x with cos2 x/sin2 x. We then use distributive property to eliminate the parentheses, so the equation now becomes sin2 x + sin2 x (cos2 x/sin2 x) = 1. Cancelling out the sin2 x in both numerator and denominator, we are left with sin2 x + cos2 x = 1, and by the first of the Pythagorean identities, the left side of the equation becomes 1 and the two sides of the equation now match.
Saketh M. answered 04/01/20
Prospective Math/CS Major with Coursework up to Complex Analysis
cot(x) = cos(x)/sin(x), so cot2(x)=cos2(x)/sin2(x)
then, sin2(x) • (1 + cos2(x)/sin2(x)) = sin2(x) + cos2(x) = 1
sinx*2 ( 1 + cotx**2) = 1
multiplying sinx**2 through:
sinx**2 + sinx**2 * cotx**2 = 1
cotx**2 = cosx**2/sinx**2
Substituting:
sinx**2 + sinx**2 * cosx**2 = 1
----------
sinx**2
The sinx**2 in the numerator and denominator cancel giving us:
sinx**2 + cosx**2 = 1, which is a known identity, so we are done.
Get a free answer to a quick problem.
Most questions answered within 4 hours.
Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.