prove that cos²π/4 + sin²π/12 = √3/4
Anonymous:
is your question right?
oh i'm extremely sorry. there is a + after cos²π/4
I think there should be -
-* yes yes '-' only. i did a terrible typing mistake. pardon me
it's ok.
___k off
Answers
Answered by
10
★Heya★
Given question
Cos² (π/4) - Sin²(π/12) = √3/4
_____________________________
Sin ( π/12 ) = Sin ( π/3 - π/4 )
= Sin (π/3)×Cos(π/4) - Cos(π/3)×Sin(π/4)
Becoz Sin ( A - B ) = Sin A × Cos B - Cos A × Sin B
= (√3/2)×(1/√2) - (1/√2)×(1/2)
= ( √3 - 1 )/2√2
So,
Sin (π/12) = ( √3 - 1 )/2√2
Sin² (π/12) =( 4 -2√3)/8
-Sin² (π/12) = ( -2 + √3 )/4
And
Cos²(π/4) = 1/2
So,
Cos²(π/4) + Sin²(π/12) =
( -2 + √3 )/4 + (1/2)
=>
= ( -2 + √3 + 2 )/4
= √3/4
Given question
Cos² (π/4) - Sin²(π/12) = √3/4
_____________________________
Sin ( π/12 ) = Sin ( π/3 - π/4 )
= Sin (π/3)×Cos(π/4) - Cos(π/3)×Sin(π/4)
Becoz Sin ( A - B ) = Sin A × Cos B - Cos A × Sin B
= (√3/2)×(1/√2) - (1/√2)×(1/2)
= ( √3 - 1 )/2√2
So,
Sin (π/12) = ( √3 - 1 )/2√2
Sin² (π/12) =( 4 -2√3)/8
-Sin² (π/12) = ( -2 + √3 )/4
And
Cos²(π/4) = 1/2
So,
Cos²(π/4) + Sin²(π/12) =
( -2 + √3 )/4 + (1/2)
=>
= ( -2 + √3 + 2 )/4
= √3/4
Answered by
1
hope it helps u............
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