Question

Find the value of Sin⁴ \(\frac{\pi}{4}\)+ 4Sin⁴\(\frac{\pi}{4}\) Sin4 \(\frac{\pi}{3}\) + Sin⁴ \(\frac{\pi}{6}\) 
1. \(\frac{7}{8}\)
2. \(\frac{-7}{2}\)
3. \(\frac{5}{8}\)
4. \(\frac{3}{2}\)

Answer 1

Correct Answer - Option 1 : \(\frac{7}{8}\)

Given:

Sin4 \(\frac{π}{4}\)+ 4Sin4 \(\frac{π}{4}\) Sin4 \(\frac{π}{3}\) + Sin4 \(\frac{π}{6}\) 

Values used:

sinπ/4 = 1/√2, sinπ/3 = √3/2, sinπ/3 = 1/2

Calculation:

Sin4 \(\frac{π}{4}\)+ 4Sin4 \(\frac{π}{4}\) Sin4 \(\frac{π}{3}\) + Sin4 \(\frac{π}{6}\) 

⇒ (1/√2)⁴ + 4 × (1/√2)4 × (√3/2)⁴ + (1/2)⁴  

⇒ 1/4 + 4 × 1/4 × 9/16 + 1/16 

⇒ 1/4 + 9/16 + 1/16 

⇒ 1/4 + 10/16 

⇒ (4 + 10)/16 

⇒ 14/16 

⇒ 7/8 

∴ The required value is 7/8.

Note: The above question is an edited version of the same question that was asked in the exam. Due to some errors, the question was declared invalid.