miscellaneous trigonometry question 7 cbse ncert 11th mathematics

miscellaneous trigonometry question 7 cbse ncert 11th mathematics

7. Prove that sin3x+sin2x-sinx = 4sin(x)cos(x/2)cos(3x/2)


using trigonometry formula trigonometry identities

sinx + siny =2sin[(x+y)/2] cos[(x-y)/2]

sinx = 2sin(x/2)cos(x/2)

and then

sinx - siny =2cos[(x+y)/2] sin [(x-y)/2]
after taking out factor

LHS=  (sin3x+sin2x) - sinx

=2sin(5x/2)cos(x/2) - 2sin(x/2)cos(x/2)

=2cos(x/2) [sin(5x/2) - sin(x/2)]

= 2cos(x/2) [ 2cos((6x/2)/2)sin((4x/2)/2) ]

=2cos(x/2) [ 2cos(3x/2)sin(x) ]


=4sin(x)cos(x/2)cos(3x/2)



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




disclaimer:
There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work