Solution to Chapter 4 Problems

1) Verify : sin (200) + 2sin(160) - cos(70) + 3sin(340) - 4cos(110) = sin(20).

    sin(π+20) + 2sin(π-20) - cos(π/2 -20) + 3sin(2π-20) - 4cos(π/2+20) =

    - sin20  + 2sin20  - sin20   - 3sin20  + 4sin20 =

                                sin(20).

==============================================

2) Verify : 3tan(130) + cot(40) - tan(230) - 5tan(310) -2cot(140) = 4tan(50).

     3tan(π-50) + tan(50)  - tan(π+50)  - 5tan(2π-50)  -2cot(π/2 +50) =

       -3tan50 + tan(50)  - tan(50)   + 5tan(50)  +2tan(50)  =

                                             4tan(50).

 ==============================================

3) Verify : 2cos(75)cos(80) + 3cos(105)sin(170) + 4sin(165)sin(190) =

 -5sin(15)sin(10).

2cos(π/2 -15)cos(π/2 -10) + 3cos(π/2 +15)sin(π - 10) + 4sin(π -15)sin(π + 10) =

2sin(15)sin(10) + 3[ -sin(15)] sin(10)  + 4sin(15)[ -sin(10)] =

2sin(15)sin(10)  -3sin(15)sin(10) -4sin(15)sin(10) =

                         -5sin(15)sin(10).

==============================================

4) Verify : cos(115) -3 sin(25) - 5sin(205) = cos(65).

                    cos(π -65) -3sin(π/2 -65) - 5sin( π + 25) =

                    - cos(65) - 3cos(65) + 5sin( 25) = 

                            - 4cos(65)  +5cos(65) = 

                                            cos(65).

==============================================

5) Verify : 3cos(310) + cos(-50) = 4cos(50).

                    3cos( -50) + cos(50) =

                        3cos(50) + cos(50)=

                                4cos(50).

==============================================

6) Verify : 2tan(60) + 3tan(240) = 5cot(30).

                2tan(60)  + 3tan(π + 60) =

                            5tan(60) =

                             5cot(30).

==============================================

7) Verify : sin(π + θ) + 2cos(π/2 - θ) -3sin(π - θ) = -2sin(θ).

                       - sin(θ)  +  2sin(θ)  - 3sin(θ)

                                    = -2sin(θ).

==============================================

8) Verify : 3tan(2π - θ) + tan(π + θ) + cot(π/2 - θ) - cot(π/2 + θ) = 0.

                    -3tanθ  + tanθ  + tanθ  + tanθ =

                                            0.

==============================================