maths Pls help trig

1 .If tanA=1/3 and tanB=1/7 (both A and B are acute),calculate 50sin(2A +B)
2.1Prove that sin2A+2cosA-2cos^3A/1+sinA =sin2A
2.2 for which values of A in the interval[-360;360] is the identity in 2.1 undefined?
3.If tanB=3/4 , 0<B<90 , prove that 4cos2B+3sin2B=4
4.Prove that (1/cos^2B)cos2B=2-1/cos^2B)
5. Write sin2A and cos2A in terms of sinA and cosA

  1. 👍 0
  2. 👎 0
  3. 👁 468
  1. 1.
    tanA = 1/3, and tanB = 1/7
    I usually construct my triangles,
    (since the fraction gives you 2 of the sides of right-angled triangles, the third can always be found using Pythagoras)

    for tanA = 1/3, sinA = 1/√10 , cosA = 3/√10
    for tanB = 1/7, sinB = 1/√50, cosB = 7/√50
    we will need sin2A and cos2A,
    sin2A = 2sinAcosA = 2(1/√10)(3/√10) = 3/50
    cos2A = cos^2 A - sin^2 A
    = 9/10 - 1/10 = 4/5
    50sin(2A+B)
    = 50(sin2AcosB + cos2AsinB)
    = 50( (3/50)(7/√50) + (4/5)(1/√50) )
    = 50(21/(50√50) + 4/(50√50)
    = 25/√50
    = 1/√2

    hey , I bet 2A +B = 45

    2. LS = (2sinAcosA + 2cosA - 2cos^3 A)/ (1+sinA)
    = cosA(2sinA + 2 - 2cos^2 A)/(1+sinA)
    = 2cosA (1 + sinA - (1 - sin^2 A) /(1+sinA)
    = 2cosA (sin^2 A + sinA) /(1+sinA)
    = 2cosA sinA (sinA + 1)/(1+sinA)
    = 2sinAcosA
    = sin 2A
    = RS

    3 make your sketch, and proceed like in #1

    4. Convert to single angle trig ratios, using your formulas

    5. All you have to do is look them up and memorize them.

    1. 👍 0
    2. 👎 0
  2. Thank u so much !!
    But I still have a question in#1 where did the 50 go?

    1. 👍 0
    2. 👎 0
  3. the denominator is 50√50

    1. 👍 0
    2. 👎 0
  4. but oops: 25/√50 = 5/√2, not 1/√2

    1. 👍 0
    2. 👎 0
  5. tanA=1/7 sin2A cos2A

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. trig

    If it is given that tan(A-B)=tanA-tanB/1+tanAtanB and tanP-1/1+tanP=tan195 find p

  2. Amaths

    prove sin(A+B)/sin(A-B)=(tanA+tanB)/(tanA-tanB)

  3. Math

    If A and B are acute angle such that SinA=8/17 and CosB=3/5.Find 1, Cos(A+B) 2, Sin(A+B) 3, Sin(A-B)

  4. Trigonometry

    If sinA + sinB = a and cosA + cosB = b, find the value of tanA-B/2

  1. math

    If TanA=k.TanB prove that (k+1)sin(A-B)=(k-1)sin(A+B).

  2. trig

    If point (3, -8) lies on the terminal side of an angle A in standard position, find: a) sinA b) tanA

  3. trignometry

    prove: sin(a+b)/cosacosb=tana+tanb

  4. Pre-calculus (Trigonometry)

    The rotating spotlight from the Coast Guard ship can illuminate up to a distance of 250 m. An observer on the shore is 500 m from the ship. HIs line of sight to the ship makes an angle of 20 degrees with the shoreline. What length

  1. maths

    if sinA+cosA=1/5, then a value of tanA/2 satisfies which of the equation? a. 2x^2-x-1 b.x^2-2x-3=0 c.2x^2-5x-3=0 d. 2x^3-7x^2+2x+3=0

  2. Trigonometry

    Prove that sin3A+sin2A-sinA = 4sinAcosA/2cos3A/2

  3. further mathematics

    Let P=(cosA sinA) (sinA cosA) Q=(cosB sinA) (sinB cosA) show that PQ=(cosA(A-B) sin(A B)) (sinA(A B) cos(A-B))

  4. Maths

    If tan inverse(x^2-y^2/x^2+y^2)=a then prove that dy/dx=x/y (1-tana/1+tana).

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