Question

the value of following sin 105°

Answer 1

Answer:

Sin 105 = ( 1 + √3 ) / 2√2

Step-by-step explanation:

Sin 105 and Sin 75 are supplementary angles. Hence both of them will have same values.

⇒ Sin 105 = Sin 75

We know that,

Sin 75 = Sin ( 45 + 30 )

Sin ( A + B ) = SinA.CosB + CosA.SinB

Hence applying this formula we get,

⇒ Sin 75 = Sin45.Cos30 + Cos45.Sin30

⇒ Sin 75 = ( 1/√2 ).( √3/2 ) + ( 1/√2 ).( 1/2 )

⇒ Sin 75 = ( √3 / 2√2 ) + ( 1 / 2√2 )

⇒ Sin 75 = ( 1 + √3 ) / 2√2

Hence Sin 105 is also equal to ( 1 + √3 ) / 2√2.

Hence evaluated !!

Answer 2

Answer:

(1+√3)/2√2

Step-by-step explanation:

sin 105°=sin 75°

sin 75°= sin(30°+45°)

sin(a+b)=sin a.cos b+cos a. sin b

sin 75°= 1/2*1/√2 + √3/2*1/√2

sin 75°= (1+√3)/2√2 = sin 105°