Math (trigonometry)

Trigonometry identities are so hard...

I need some help proving these identities:
*Oh, and I'm only in grade 11, so the identities we use are quotient identity and Pythagorean identity.

sinx/(sinx + cosx) = tanx/(1 + tanx)

cos^2x - sin^2x = 2cos^2x - 1

Thanks!
Lucy

  1. 👍 0
  2. 👎 0
  3. 👁 94
asked by Lucy
  1. By inverting the fractions (a perfectly legal operation), the first equation can be converted to
    (sin x + cos x)/sin x = (1 + tan x)/x
    1 + cot x = 1 + 1/tan x
    = 1 + cot x

    In the second problem, substitute 1 - cos^2 x for sin^2 x on the left side.

    1. 👍 0
    2. 👎 0
    posted by drwls
  2. Thanks for your help!

    I understand the second problem now.
    Except I'm confused about what you did in the first problem. We haven't learned anything about cotx yet...

    I inverted the fractions, though and ended up with:

    (sin x + cos x) / sin x = (1 + tan x) / tanx
    (I'm just wondering...why did you write (1 + tan x) / x on the left side?)

    Then simplifies to... cos x = 1 ??

    I'm confused... :S

    1. 👍 0
    2. 👎 0
    posted by Lucy
  3. *Sorry, should be:

    I'm just wondering...why did you write (1 + tan x) / x on the *right* side?

    Instead of (1 + tan x) / tan x?

    1. 👍 0
    2. 👎 0
    posted by Lucy
  4. SOH CAH TOA... IT'S sin=opposite over hypotenus..... Cos=ajacent over hypotenus.... Tan=opposite over ajacent

    1. 👍 0
    2. 👎 0
  5. SOH CAH TOA... IT'S sin=opposite over hypotenus..... Cos=ajacent over hypotenus.... Tan=opposite over ajacent..... When you want to fine thiter or any angle

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Pre-Calculus

    This question has me stuck. Use the Pythagorean identity sin^2 Θ + cos^2 Θ = 1 to derive the other Pythagorean identities, 1 + tan^2 Θ = sec^2 Θ and 1 + cot^2 Θ = csc^2 Θ. Discuss how to remember these identities and other

    asked by Iris on September 29, 2016
  2. discrete mathematics

    can you give an example of indirect proof in trigonometry using the identities.

    asked by angelyn on August 13, 2015
  3. Trig

    How do you express sin4x as a trigonometric funcition of x using the identities? I think that you are supposed to start with the sine sum identity and then use the double angle identities for sin2A and cos2A, but after that I get

    asked by Taylor on February 17, 2010
  4. Trigonometry

    This is more of an opinion question: I'm working on Verifying Identities but I always have trouble knowing where to start. Once my teacher points it out i'm like "oh, duh" but on my own I have not the slightest idea on how to

    asked by Izza on March 25, 2008
  5. Math

    Trigonometry Identities problem: Prove the following; (tan^2x)(cos^2x) = (sec^2x - 1)(1-sin^4x) ÷ (1+sin^2x)

    asked by hhfo on July 26, 2011
  6. pre-calculus

    I am having trouble with trigenometric identities I cannot figure it out for example sin³x+sin²xcos²x, could I get the steps to figure it out? And also how to do the equations and proving of trid id's. Please help. Thank you

    asked by devry on January 5, 2010
  7. Trig

    Proving Identities: 2 columns (tan + cot)^2 = sec^2 + csc^2 I'm having trouble breaking down the left side to = the right side.. Any help please

    asked by Don on January 8, 2012
  8. math

    The Pythagorean Theorem gives the relationship between the sides of a right triangle. The following identities show the relationships between the trigonometric functions of a particular angle. sin2 θ + cos2 θ = 1 tan2 θ + 1 =

    asked by rick on May 12, 2012
  9. Trigonometry - Proofs

    Prove that the average of the numbers n sin (n degrees) (n = 2, 4, 6, ... 180) is cot (1 degree) Hint: Express everything in terms of sin and cos. Can you rearrange the result into a form that allows you to use some of the

    asked by Sam on November 12, 2013
  10. Pre-Cal

    [Note: I'm still having issues with identities with regard to trig] Verify the Trig. identities: (a). cot(x+y)=(cotxcoty-1)/(cotx+coty) (b). sin0(cot0+tan0)=sec0 [Note: 0=theta symbol]

    asked by Amber on July 11, 2016

More Similar Questions