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

Karissa Sosa 2022-04-06 Answered
Prove this trigonometry equation: sin 40 sin 50 is equal to 1 2 cos 10
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Answers (2)

Ellie Meyers
Answered 2022-04-07 Author has 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.
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measgachyx5q9
Answered 2022-04-08 Author has 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.
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