Factorizing help

Question

Show step by step why/how the left side equals the right side.

 

Answer 1

Left hand side identity = sin²x - 6 sinx + 12

= sin²x - 6 sinx +  9 + 3

= sin² x  - 6sinx + 9 + 3

= sin² x  - 6sinx + 9 + 3

= sin² x  - 2 (3) sinx + 3² + 3

{ Apply the formula (a - b)² = a² + b² + 2ab, In this case a = sinx , b = 3.}

= (sinx - 3)² + 3

= Right hand side identity.