Question

5) Find the value of Sin 75°
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Answer 1

Step-by-step explanation:

sin(A+B) ≡ sin(A)cos(B) + sin(B)cos(A)

⇒ sin(75°) = sin(30+45)° = sin(30°)cos(45°) + sin(45°)cos(30°)

= ½ × 1/√2 + 1/√2 ×(√3)/2 = 1/(2√2) + (√3)/(2√2)

= (1+√3)/(2√2)

Answer 2

Answer:

Sin 75° = (√3 + 1)/2√2

Solution:

We have to find the value of Sin 75°. Let us some Trigonometric compound ratios before solving this problem.

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

Sin 75° can be written as Sin(45° + 30°). We will solve the above expression with the help of trigonometric compound ratios.

Sin 75°

0r, Sin(45° + 30°)

0r, Sin45°.Cos30° + Cos45°.Sin30°

0r, (1/√2. √3/2) + ( 1/√2 + 1/2)

0r, {(√3)/2√2 + (2+√2)/2}

0r, (√3 + 1)/2√2

• Therefore, the required value of Sin 75° is (√3 + 1)/2√2

Therefore, the required value of Sin 75° is (√3 + 1)/2√2