Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

find the value of sin20degree*sin40degree*sin80degree =

find the value  of sin20degree*sin40degree*sin80degree =

Grade:11

3 Answers

Lucky
27 Points
4 years 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.
Arun
25763 Points
4 years 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
 
 
Regards
Arun (askIITians forum expert)
Avinash
52 Points
3 years 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

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free