Prove this trigonometry equation: sin &#x2061;<!-- ⁡ --> 40 &#x2218;<!-- ∘ -->

Karissa Sosa

Karissa Sosa

Answered question

2022-04-06

Prove this trigonometry equation: sin 40 sin 50 is equal to 1 2 cos 10

Answer & Explanation

Ellie Meyers

Ellie Meyers

Beginner2022-04-07Added 15 answers

Taking L.H.S.
s i n 40 ° s i n 50 ° or s i n 50 ° s i n 40 °
We know the identity, s i n A s i n B = 1 2 ( c o s ( A B ) c o s ( A + B ) )
Here we consider A=50° and B=40°
Then, s i n 50 ° s i n 40 ° = 1 2 ( c o s ( 50 ° 40 ° ) c o s ( 50 ° + 40 ° ) )
= 1 2 ( c o s 10 ° c o s 90 ° )
= 1 2 ( c o s 10 ° 0 ) ( c o s 90 ° = 0 )
= 1 2 c o s 10 °
L.H.S.=R.H.S.
measgachyx5q9

measgachyx5q9

Beginner2022-04-08Added 2 answers

Here,
L . H . S = s i n 40 ° . s i n 50 °
= 2 2 . s i n 40 ° . s i n 50 °
= 1 2 ( c o s 10 ° c o s 90 ° )
= 1 2 c o s 10 ° = R. H . S
Proved.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?