Find the value of sin 75 degre and cos 75 degre
Answers
Answer:sin(75
∘
)=sin(45+30)
∘
= sin30 cos45 + sin45 cos30
=
2
1
×
2
1
+
2
1
×
2
3
=
2
2
1
+
2
2
3
=
2
2
1+
3
Step-by-step explanation:
Answer:
Answer: (√3 + 1)/ 2√2
Sin 75 we can write it as
Sin 75 = Sin(45+30)…………………..(1)
By applying the formula
Sin (A + B) = Sin A. Cos B + Cos A. Sin B
Sin (45 + 30) = Sin 45. Cos 30 + Cos 45. Sin 30…………………..(2)
Sin Values
sin 0° = √(0/4) = 0
sin 30° = √(1/4) = ½
sin 45° = √(2/4) = 1/√2
sin 60° = √3/4 = √3/2
cos 90° = √(4/4) = 1
Cos Values
cos 0° = √(4/4) = 1
cos 30° = √(3/4) = √3/2
cos 45° = √(2/4) = 1/√2
cos 60° = √(1/4) = 1/2
cos 90° = √(0/4) = 0
Substitute the value of sin 30, sin 45, cos 30 and cos 45 degrees, then equation (2) will becomes
Sin (45 + 30) = Sin 45. Cos 30 + Cos 45. Sin 30
Sin (45 + 30) = 1/√2 . √3/2 + 1/√2 . 1/2
Sin (45 + 30) = (√3 + 1) / 2√2
Hence the value of Sin 75 degree is equal to (√3 + 1) / 2√2.