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3 years ago

Prove that sin20 sin40 sin60 sin80=3/16

1 answer:

6 0

sin20 * sin40 * sin60 * sin80

since sin 60 = √3/2

√3/2 (sin 20 * sin 40 * sin 80)
√3/2 (sin 20) [sin 40 * sin 80]

Using identity: sin A sin B = (1/2) [ cos(A - B) - cos(A + B) ]

√3/2 (sin 20) (1 / 2) [cos 40 - cos 120]
√3/4 (sin 20) [cos 40 + cos 60]

Since cos 60 = 1/2:

√3/4 (sin 20) [cos 40 + (1/2)]
√3/4 (sin 20)(cos 40) + √3/8 (sin 20)

Using identity: sin A cos B = 1/2 [ sin(A + B) + sin(A - B) ]

√3/4 (1 / 2) [sin 60 + sin (-20)] + √3/8 (sin 20)

Since sin 60 = √3/2

√3/8 [√3/2 - sin 20] + √3/8 (sin 20)
3/16 - √3/8 sin 20 + √3/8 sin 20

Cancelling out the 2 terms:
3/16

Therefore, sin20 * sin40 * sin60 * sin80 = 3/16

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3 years ago

Read 2 more answers

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3 years ago

Help please n/9 + 2/3 = -2/3

Free_Kalibri [48]

Answer:

n = - 12

Step-by-step explanation:

n/9 + 2/3 = - 2/3

n/9 = - 2/3 - 2/3

n/9 = - 4/3

n = 9(- 4/3)

n = -36/3

n = - 12

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2 years ago

I need help really badly please help me I’ll give brainiest

Mashutka [201]

Answer:

75%

Step-by-step explanation:

15+15+25+5=60

15/60=25%

100%-25% = 75%

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2 years ago

2. Solve each given equation and show your work. Tell whether each equation has one solution, an infinite number of solutions, o

Brut [27]

Hello!

To solve algebraic equations, we need to use SADMEP. SADMEP is an acronym used only solve for x in algebraic equations. SADMEP is expanded to be: subtraction, addition, division, multiplication, exponents, and parentheses.

(a) 4 + 2(-1) = 10 + 2 (multiply)

4 + -2 = 10 + 2 (add)

2 = 12

This equation has no solutions because 2 is never equal to 12.

(b) 30 = 10 - (6 + 10) (simplify the parentheses)

30 = 10 + -1(16) (multiply)

30 = 10 - 16 (simplify)

30 = -6

This equation has no solutions because 30 and -6 is never equal to each other.

8x = 4x + 4x + 10(x - x) (simplify [add and subtract])

8x = 8x + 10(0) (multiply)

8x = 8x

This equation has an infinite number of solutions because if you substitute any value into the original equation, both sides of the equation will be always equal.

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2 years ago