How do I solve this problem? (Algebra 2)?

Comments

• iceman

  June 2021

  csc(x) * (sec(x) - cos(x))

  = 1/sin(x) * (1/cos(x) - cos(x))

  = 1/sin(x) * (1 - cos^2(x))/cos(x)

  = sin^2(x)/((sin(x) * cos(x))

  = sin(x)/cos(x)

  = tan(x)
• jeremy-w

  June 2021

  I will use x instead of alpha. Remember that csc x = 1/sin(x) and sec x = 1/cos(x). Making these substitutions gives

  (1/sin(x))(1/cos(x) - cos(x))

  Multiply the -cos(x) by cos(x)/cos(x) to get a common denominator

  (1/sin(x))(1/cos(x) - cos(x)^2/cos(x))

  Combine the terms in the right parenthesis

  = (1/sin(x))[(1-cos(x)^2)/(cos(x))]

  Use the sin^2 + cos^2 = 1 identity to get

  = (1/sin(x))[sin(x)^2/cos(x)]

  One set of sines cancel, leaving us with

  = sin(x)/cos(x)

  Which is equal to

  = tan(x)
• vvvvv

  June 2021

  Just use the Trigonometric Identities:

  cscθ(secθ-cosθ)

  1/sinθ(1/cosθ-cosθ)

  1/sinθcosθ-cosθ/sinθ

  1/sinθcosθ-cotθ
• anonymous

  June 2021

  cscα=1/sinα secα=1/cosα

  then the equation is equivalent to 1/sinα(1/cosα-cosα)

  then =1/sinαcosα - cotα

  =1/2sin2α -cotα
• anonymous

  June 2021

  cscα(secα - cosα) = cscα*secα - cscα*cosα;

  cscα = 1/sinα

  secα = 1/cosα

  Then:

  1/sinα * 1/cosα - 1/sinα * cosα = 1/sinα cosα - cosα/sinα.

  cosα/sinα = cotα

  sinα*cosα = sin(2α)/2

  Then:

  1/sin(2α)/2 + cotα = 2/sin(2α) + cotα. That's it.

  cot - cotangent.
• anonymous

  June 2021

  while the exponent is a minus huge type then the huge type on which the exponent has been positioned would be reciprocaled (reversed). then you fairly gets, (a million/-2)^2 =(a million/-2)(a million/-2) =(a million/-4) hence ,the respond is a million/-4 = -a million/4 or -0.25
• anonymous

  June 2021

  let alpha = x (for sake of typing)

  cscx = 1/sinx

  secx = 1/cosx

  simplify cscxsecx - cscxcosx

  so 1/sinxcosx - cotx

  personally, i feel it is simpler as cscxsecx - cotx, but a teacher might argue the other way
• jonathan-owen_60b83789cc828

  June 2021

  csc(x) * (sec(x) - cos(x))

  csc(x)sec(x) - cos(x)(csc(x))

  csc = 1/sin

  sec = 1/cos

  (1/(sin(x)*cos(x)) - cos(x)/sin(x)

  (1/(sin(x)*cos(x))) - cot(x)
• tanya-wilkinson_60b8378aefe46

  June 2021

  csc(α)(sec(α) - cos(α))=

  = (1/sin(α))(1/cos(α) - cos(α))=

  = (1/sin(α))(1 - cos²(α))/cos(α)=

  = sin²(α)/(cos(α)sin(α))=

  = sin(α)/cos(α)=tg(α)