Question

The
value of sin (15) is​

Answer 1

Step-by-step explanation:

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Answer 2

Question:

Find the value of sin15° .

Answer:

(√3 – 1) / 2√2

Note:

• sin(A+B) = sinAcosB + cosAsinB

• sin(A-B) = sinAcosB – cosAsinB

• cos(A+B) = cosAcosB – sinAsinB

• cos(A-B) = cosAcosB + sinAsinB

• sin30° = 1/2

• sin45° = 1/√2

• cos30° = √3/2

• sin45° = 1/√2

Solution:

sin15° = sin(45°-30°)

= sin45°cos30° – cos45°sin30°

{ sin(A-B) = sinAcosB – cosAsinB }

= (1/√2)•(√3/2) – (1/√2)•(1/2)

= √3/2√2 – 1/2√2

= (√3 – 1) / 2√2

Hence,

The required value of sin15° is :

(√3 – 1) / 2√2