Question

cos 2x sin x + cos 6x sin 3x by sin 2x sin x + sin 6x sin x = cot 5x ​

Answer 1

• Well, do as it says and use the first part. You already have that
• sin(2x)+sin(4x)+sin(6x)=(1+2cos(2x))sin(4x)
• So for the case of sin(x)(sin(2x)+sin(4x)+sin(6x)), just plug in the result you got from part I:

• sin(x)(sin(2x)+sin(4x)+sin(6x))=sin(x)(1+2cos(2x))sin(4x)=(sin(x)+2sin(x)cos(2x))sin(4x)=(sin(x)+2sin(x)(1−2sin(x)2))sin(4x)=(3sin(x)−4sin(x)3)sin(4x)=sin(3x)sin(4x)
• Note that the last identity that I used was the triple angle identity:

• 3sin(x)−4sin(x)3=sin(3x)

For the third part, you want sin(π12), but you already know sin(π6)=12, sin(π3)=3√2, sin(π4)=2√2, and sin(π2)=1. So, plug in π12 for x in equation II and solve for it, since every other equation will yield a known value.

Answer 2

Answer:

This is the answer I hope you understood this