Please someone help me to prove this...

Step-by-step explanation:

cos 20° cos 40° cos 60° cos 80°

Simplify cos 60° to ½.

½ cos 20° cos 40° cos 80°

We can use double angle formula, sin(2θ) = 2 sin θ cos θ.  Multiply and divide by 2 sin 20°.

½ (2 sin 20° cos 20° cos 40° cos 80°) / (2 sin 20°)

½ (sin 40° cos 40° cos 80°) / (2 sin 20°)

Multiply and divide by 2 and use double angle formula again.

½ (2 sin 40° cos 40° cos 80°) / (4 sin 20°)

½ (sin 80° cos 80°) / (4 sin 20°)

Multiply and divide by 2 and use double angle formula again.

½ (2 sin 80° cos 80°) / (8 sin 20°)

½ (sin 160°) / (8 sin 20°)

Use phase shift identity sin θ = sin(180−θ).

½ (sin 20°) / (8 sin 20°)

1/16

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3