Question

Find the value of sin 15 + cos

Answer 1

Answer:

Method 1:

Trigonometric identities used:

• sin²A + cos²A = 1

• sin(2A) = 2 sinA cosA

sin15° + cos15°

= √(sin15° + cos15°)²

= √(sin²15° + 2 sin15° cos15° + cos²15°)

= √[(sin²15° + cos²15°) + 2 sin15° cos15°]

= √[1 + sin30°]

= √[1 + 1/2]

= √[3/2]

= √[(3/2) × (2/2)]

= √6/2

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Method 2:

Trigonometric identities used:

• sin(A - B) = sinA cosB - cos A sinB

• cos(A - B) = cosA cosB + sinA sinB

sin15° + cos15°

= sin(45° - 30°) + cos(45° - 30°)

= sin45°cos30° - cos45°sin30° + cos45°cos30° + sin45° sin30°

= (√2/2)(√3/2) - (√2/2)(1/2) + (√2/2)(√3/2) + (√2/2)(1/2)

= 2(√2/2)(√3/2)

= √6/2