taking the angle in degree measure
sin(0)=0
cos(0)=1
tan(0)=0
sin(90)=1
cos(90)=0
tan(90)=infinity
sin(30)=1/2
cos(30)=[( sqrt(3) ) / 2]
tan(30)=1 / {sqrt(3)}
sin(60)=[( sqrt(3) ) / 2]
cos(60)=1/2
tan(60)= {sqrt(3)}
sin(45) ={ 1 / [ sqrt(2) ] }
cos(45) ={ 1 / [ sqrt(2) ] }
tan(45)=1
1.Prove that 2cos(pi/13)cos(9pi/13)+cos (3pi/13)+cos(5pi/13) = 0
solution
2. Prove that ( sin3x + sinx ) sinx + (cos3x - cosx) cosx = 0
solution
3. Prove that (cosx +cosy)^2 + ( sinx - siny )^2 = 4 { cos[(x+y)/2] }^2
solution
4. Prove that (cosx - cosy)^2 + ( sinx - siny )^2 = 4 { sin[(x-y)/2] }^2
solution
5.Show that sinx +sin3x+ sin5x +sin7x = 4cosx cos2x sin 4x
solution
6. Show that [sin7x+sin5x +sin9x+sin3x] / [cos7x+cos5x+cos9x+cos3x] = tan6x
solution
7. Prove that sin3x+sin2x-sinx = 4sin(x)cos(x/2)cos(3x/2)
solution
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