Question

prove that cos (π/12)-sin(π/12)=1/√2

Answer 1

Hey there !

Solution:

We know that,

360 = 2π

=> π = 360 / 2 = 180°

According to the Question,

Cos ( π / 12 ) - Sin ( π / 12 ) = 1 / √2

Taking the Left Hand Side into consideration we get,

=> Cos ( 180 / 12 ) - Sin ( 180 / 12 )

=> Cos ( 15 ) - Sin ( 15 )

Let us simplify the above equation. We get,

=> Sin ( 90 - 15 ) - Sin 15 )

=> Sin 75 - Sin 15

We know that,

Sin C - Sin D = 2 Cos [ ( A + B ) / 2 ] . Sin [ ( A - B ) / 2 ]

=> Sin 75 - Sin 15 = 2 Cos ( 75 + 15 ) / 2 . Sin ( 75 - 15 ) / 2

=> Sin 75 - Sin 15 = 2 Cos 90 / 2 . Sin 60 / 2

=> Sin 75 + Sin 15 = 2 Cos 45 . Sin 30

=> Sin 75 - Sin 15 = 2 × 1 / √2 × 1 / 2

=> Sin 75 - Sin 15 = 1 / √2.

Hence Proved !

Hope my answer helped !

Answer 2

Answer is as follows