Question

The value of 4(sin⁴30° + cos⁴30°) - 3(sin²45° - 2cos²45°) is:
1. 2
2. 1
3. 4
4. 0

Answer 1

Correct Answer - Option 3 : 4

Given:

? = 4(sin430° + cos430°) - 3(sin245° - 2cos245°)

Concept:

sin 30° = 1/2

cos 30° = √3/2

sin 45° = 1/√2

cos 45° = 1/√2

Calculation:

⇒ ? = 4(sin430° + cos430°) - 3(sin245° - 2cos245°)

⇒ ? = 4[(1/2)⁴ + (√3/2)⁴] - 3[(1/√2)² - 2(1/√2)²]

⇒ ? = 4[1/16 + 9/16) - 3(1/2 - 1)]

⇒ ? = 4[10/16] + 3/2

⇒ ? = 5/2 + 3/2

⇒ ? = 4

∴ 4(sin430° + cos430°) - 3(sin245° - 2cos245°) = 4