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`        find the value  of sin20degree*sin40degree*sin80degree =`
one year ago

```							For solving such type of questions you can refer to r.d Sharma of 11 class and chapter 8 (transformation formula) the solution is way too long but I get my answer = square root of 3 divided by 8.
```
one year ago
```							I'm assuming that you know this: sin(A+B) = sin A cos B + cos A sin B Step number 1: write sin(40) as sin(60-20) write sin(80) as sin(60+20) since 60 degrees is a remarkable angle, you know that sin(60) = √(3)/2 Step 2: you have this: sin(20)•sin(60-20)•sin(60+20) - Simplify sin(60-20)•sin(60+20) sin(60-20) = sin60•cos20 - sin20•cos60 sin(60+20)= sin60•cos20 + sin20•cos60 - multiply them: = sin²60•cos²20 - sin²20•cos²60 Step 3: - you know that sin²A+cos²A=1, - so, cos²A = 1 - sin²A - Simplify sin²60•cos²20 - sin²20•cos²60 = sin²60•(1-sin²20) - sin²20•(1-sin²60) = sin²60- sin²20•sin²60 - sin²20 + sin²20•sin²60 = sin²60 - sin²20 = 3/4 - sin²20 Step 4: This is what we have now: = sin20•(3/4 - sin²20) = [1/4]•(3sin20 - 4sin³20) - note that 4sin³20 comes from putting [(3sin20)/4]-sin³20 on the same base Step 5: you need to know that sin(3A) = 3sin(A) - 4sin³(A) (multiple angle relations) - so, (3sin20 - 4sin³20) = sin60 Step 6: now you have this: = [1/4]•sin60 = [1/4]•[√(3)/2) =√(3)/8  RegardsArun (askIITians forum expert)
```
one year ago
```							We all know that.   Sinx.sin(60-x)sin(60+x)=1/4sin3xHere x=20Therefore sin20.sin40.sin80=1/4sin3×20                                        =1/4Sin60                                           =1/4×√3/2                                             =√3/8 Sin20.sin40.sin80=√3/8
```
one year ago
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