Question

sin ²30° + sin ²45° & sin²60° + sin² 90°​

Answer 1

Answer:

sin² 30° + sin² 45° + sin² 60° + sin² 90°                            

= (½)² + (1/√2√)² + (√3/2)² + (1)²

= ¼ + ½ + ¾ + 1

= ¼ + ¾ + ½ + 1

= (1 + 3)/4 + (1+ 2)/2

[By taking L.C.M]

= 4/4 + 3/2

= 1 + 3/2

= (2 + 3)/2 = 5/2

[ By taking L.C.M]

sin² 30° + sin² 45° + sin² 60° + sin² 90° = 5/2

[sin 60° = √3/2 ,  sin 45° =1/√2  , sin 90° = 1]                                    

Hence, sin² 30° + sin² 45° + sin² 60° + sin² 90° = 5/2