Question

Find the value of sin36°sin72°sin108°sin144°

Answer 1

Answer:

=> sin36°sin72°sin108°sin144°

=> sin36°sin72°sin(180°-72°)sin(180°-36°)

=> sin36°sin72°sin{(90°×2)-72°}sin{(90°×2)-36°}

=> sin36°sin72°sin72°sin36°

=> sin²36°sin²72°

=> [√(10-2√5)/4]²×[√(10+2√5)/4]²

=> (10-2√5)/16×(10+2√5)/16

=> (100-20)/(16×16)

=> 80/(16×16)

=> 5/16