Question

please help me in the above question with explanation ​

Answer 1

Step-by-step explanation:

sin²A - sin² B = sin (A+B) × sin (A-B)

$= sin(52.5 + 22.5) \times sin(52.5 - 22.5) \\ = sin(75) \times sin(30) \\ = \frac{ \: \sqrt{3 } + 1\:}{2 \sqrt{2} } \times \frac{1}{2} \\ = \frac{ \sqrt{3 } + 1}{4 \sqrt{2} } \\ = \frac{ \sqrt{3 } + 1}{4 \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ = \frac{ \sqrt{2} ( \sqrt{3} + 1)}{4 \times 2} \\ = \frac{ \sqrt{2}( \sqrt{3} + 1) }{8}$

hope it helped you