Answer :
To calculate sin 75 degrees
Use identity sin(a+b)=sin(a)cos(b) + sin(b)cos(a)
sin 75 = sin(30+ 45)
i.e. sin30cos45 +sin45cos30
1/2*root2/2 + root3/2*root2/2
=root2/4+root6/4
=(root2 + root6)/4
Calculating with calculator we get
sin 75 (approximately)=0.9659
Use identity sin(a+b)=sin(a)cos(b) + sin(b)cos(a)
sin 75 = sin(30+ 45)
i.e. sin30cos45 +sin45cos30
1/2*root2/2 + root3/2*root2/2
=root2/4+root6/4
=(root2 + root6)/4
Calculating with calculator we get
sin 75 (approximately)=0.9659
sin 75=sin(45 + 30)
=(sin 45 ×.cos 30) + (cos 45 × sin 30) As[sin(x+y)= sin x.cos y+ sin y.cos x]
=(1÷√2)×(√3÷2) + (1÷√2)×(1÷2)
=(√3+1)÷2√2 {ans}
=(sin 45 ×.cos 30) + (cos 45 × sin 30) As[sin(x+y)= sin x.cos y+ sin y.cos x]
=(1÷√2)×(√3÷2) + (1÷√2)×(1÷2)
=(√3+1)÷2√2 {ans}