Question

Sin 10° sin 50° sin 70°=1/8

Answer 1

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Given that

Sin 10° Sin 50° sin 70° = 1/8
Now we multiply upper & bottom both side 2/2

then

➡ 1/2 (2sin 10° sin50° 70°)

➡ 1/2 sin10°( 2sin70° sin50°)

we know that
2 sinA sinB = cos (A-B) - cos (A+B)

Then

➡ 1/2 sin 10° ( cos 20° - cos 120°)

➡ 1/2 sin 10° ( cos 20° - cos (90°+30°))

➡ 1/2 sin 10° ( cos 20° +1/2)

➡ 1/2 sin 10° cos 20° +1/4 sin 10°

again we multiply both upper & bottom side 2/2 so

➡ 1/4 ( 2 sin 10° cos 20°). + 1/4 sin 10°

we know that
2 sinA cos B = sin (A+B) - sin (A- B)

➡ 1/4 (sin 30° - sin 10°) + 1/4 sin 10°

➡ 1/4 sin 30° - 1/4 sin 10° + 1/4 sin 10°

we know sin 30° = 1/2

➡ 1/4 × 1/2

➡ = 1/8 hence proved

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Answer 2

Answer: 1/8

Step-by-step explanation:

Given : sin 10° sin 50° sin 70°

To find : The value of sin 10° sin 50° sin 70°

Solution :

Given : sin 10° sin 50° sin 70° = 1/8

L.H.S : sin 10° sin 50° sin 70°

Multiplying  and dividing by 2:

⇒ 1/2 (2sin 10° sin50° sin 70°)

⇒ 1/2 sin10°( 2sin70° sin50°)

We know that,

2 sinA sinB = cos (A-B) - cos (A+B)

⇒ 1/2 sin 10° ( cos 20° - cos 120°)

⇒ 1/2 sin 10° ( cos 20° - cos (90°+30°))

⇒ 1/2 sin 10° ( cos 20° +1/2)

⇒ 1/2 sin 10° cos 20° +1/4 sin 10°

Multiplying and dividing by 2 :

⇒ 1/4 ( 2 sin 10° cos 20°). + 1/4 sin 10°

We know that

2 sinA cos B = sin (A+B) - sin (A- B)

⇒ 1/4 (sin 30° - sin 10°) + 1/4 sin 10°

⇒ 1/4 sin 30° - 1/4 sin 10° + 1/4 sin 10°

[ sin 30° = 1/2 ]

⇒ 1/4 × 1/2

⇒ 1/8 = R.H.S

∴ Hence Proved

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