Math

Which of the following counterexamples proves that sinxtanx=cosx is not a trigonometric identity? Select all that apply.
-2π
-3π
-3π/4
-π/4

  1. 👍 1
  2. 👎 0
  3. 👁 467
  1. For x = - 2 π

    sin ( - 2 π ) = 0 , cos ( - 2 π ) = 1 , tan ( - 2 π ) = 0

    sin ( - 2 π ) ∙ tan ( - 2 π ) = 0 ∙ 0 = 0 ≠ cos ( - 2 π )

    0 ≠ 1

    For x = - 3 π

    sin ( - 3 π ) = 0 , cos ( - 3 π ) = - 1 , tan ( - 3 π ) = 0

    sin ( - 3 π ) ∙ tan ( - 3 π ) = 0 ∙ 0 = 0 ≠ cos ( - 3 π )

    0 ≠ - 1

    For x = - 3 π / 4

    sin ( - 3 π / 4 ) = -√ 2 / 2 , cos ( - 3 π / 4 ) = - √ 2 / 2 , tan ( - 3 π / 4 ) = 1

    sin ( - 3 π / 4 ) ∙ tan ( - 3 π / 4 ) = -√ 2 / 2 ∙ 1 = - √ 2 / 2 = cos ( - 3 π / 4 )

    - √ 2 / 2 = - √ 2 / 2

    For x = - π / 4

    sin ( - π / 4 ) = -√ 2 / 2 , cos ( - π / 4 ) = √ 2 / 2 , tan ( - π / 4 ) = - 1

    sin ( - π / 4 ) ∙ tan ( - π / 4 ) = -√ 2 / 2 ∙ ( - 1 ) = √ 2 / 2 = cos ( - π / 4 )

    √ 2 / 2 = √ 2 / 2

    So x = - 2 π and x = - 3 π proves that

    sin x ∙ tan x = cos x is not a trigonometric identity,

    1. 👍 0
    2. 👎 0
  2. Seems like Reiny already helped you with this, but here goes again.
    If it is an identity, then all of the values suggested should work.
    So, does
    sin(-2π)*tan(-2π) = cos(-2π) ?
    0*0 = 1 ?
    Nope. So, using -2π proves it is not an identity.

    Now you try the others. If you get stuck, come on back and show what you got.

    1. 👍 0
    2. 👎 0
  3. Also you can do this:

    sin x ∙ tan x = cos x

    sin x ∙ sin x / cos = cos x

    sin² x / cos = cos x

    Multiply both sides by cos x

    sin² x = cos² x

    For x = - 2 π

    sin ( - 2 π ) = 0 , cos ( - 2 π ) = 1

    sin² ( - 2 π ) = 0 ≠ cos² ( - 2 π )

    0 ≠ 1²

    0 ≠ 1

    For x = - 3 π

    sin ( - 3 π ) = 0 , cos ( - 3 π ) = - 1 ,

    sin² ( - 3 π ) = 0 ≠ cos² ( - 3 π )

    0 ≠ ( - 1 )²

    0 ≠ 1

    For x = - 3 π / 4

    sin ( - 3 π / 4 ) = -√ 2 / 2 , cos ( - 3 π / 4 ) = - √ 2 / 2

    sin² ( - 3 π / 4 ) = ( -√ 2 / 2 )² = 2 / 4 = 1 / 2 =

    cos² ( - 3 π / 4 ) = ( - √ 2 / 2 )² = 2 / 4 = 1 / 2

    1 / 2 = 1 / 2

    For x = - π / 4

    sin ( - π / 4 ) = -√ 2 / 2 , cos ( - π / 4 ) = √ 2 / 2

    sin² ( - π / 4 ) = ( -√ 2 / 2 )² = 2 / 4 = 1 / 2 =

    cos² ( - π / 4 ) = ( - √ 2 / 2 )² = 2 / 4 = 1 / 2

    1 / 2 = 1 / 2

    So x = - 2 π and x = - 3 π proves that

    sin x ∙ tan x = cos x is not a trigonometric identity.

    1. 👍 0
    2. 👎 0
  4. Or, having arrived at
    sin² x = cos² x
    then
    tan² x = 1
    which is only true for odd multiples of π/4
    so, for -2π and -3π it won't work

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math, please help

    Which of the following are trigonometric identities? (Can be more then one answer) tanx cosx cscx = 1 secx-cosx/secs=sin^2x 1-tanxtany=cos(x+y)/cosxcosy 4cosx sinx = 2cosx + 1 - 2sinx Find all solutions to the equation cosx

    asked by Jill on January 14, 2014
  2. Pre-Calc

    Establish the identity. sinx + cosx/sinx - cosx = 1+2sinxcosx/2sin^2x-1

    asked by Brittany on March 30, 2009
  3. Math

    Use a counter example to show that cos(x+y)= cosx +cosy is not an identity

    asked by Brandon on November 24, 2009
  4. trigonometry

    verify the identity: (cosx/1+sinx) + (1+sinx/cosx) = 2secx

    asked by mikey on October 11, 2012
  5. Math

    verify the identity (1-cosx)/(sinx)+(sinx)/(1-cosx)=2cscx Thank you!

    asked by Anonymous on November 27, 2013
  1. Math

    Radical ((1-sinx)/(1+sinx))= (1-sinx)/cosx (absolute) Identity identity

    asked by Anonymous on December 11, 2014
  2. Math

    Can you find (a) a sine graph which touches the lines y = 3 and y = 1? (b) a cosine graph which crosses the x-axis at x = 1 and x = −1? (c) a tangent graph which passes through the point (π/3, 0) and for which the line x= π/2

    asked by Anna on May 24, 2019
  3. Pre-Calc

    Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= tanx + secx My work so far: (sinx/cosx + 1/cosx + cosx/cosx)/(sinx/cos x - 1/cosx + cosx/cosx)= tanx + cosx (just working on the left side) ((sinx + 1 -

    asked by Dave on January 2, 2007
  4. Precalc

    rewrite sinxtanx/(cosx+1) as an expression that doesn't involve a fraction.

    asked by Sophia on October 23, 2012
  5. Advanced Functions/Precalculus

    Trigonometry Questions 1. Using a compound angle formula, demonstrate that sin2π/3 is equivalent to sin π/3 2. The expression sinπ is equal to zero, while the expression 1/cscπ is undefined. Why is the identity

    asked by john on December 5, 2013
  6. Math - Pre- Clac

    Prove that each of these equations is an identity. A) (1 + sinx + cos x)/(1 + sinx + cosx)=(1 + cosx)/sinx B) (1 + sinx + cosx)/(1 - sinx + cosx)= (1 + sin x)/cosx Please and thankyou!

    asked by Jonathan on December 14, 2009

You can view more similar questions or ask a new question.