Question

Prove that:cos20°cos40°cos80°=1/8​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the double angle identity for sine

sin2x = 2sinxcosx

Consider left side

cos20°cos40°cos80°

= $\frac{1}{2sin20}$ (2sin20°cos20°)cos40°cos80°

= $\frac{1}{4sin20}$ (2sin40°cos40°)cos80°

= $\frac{1}{4sin20}$ (sin80°cos80° )

= $\frac{1}{8sin20}$ (2sin80°cos80° )

= $\frac{1}{8sin20}$ . sin160°

= $\frac{1}{8sin20}$ . sin(180 - 20)°

= $\frac{1}{8sin20}$ . sin20°

= $\frac{1}{8}$ = right side , thus proven

Answer 2

Step-by-step explanation:

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