3. প্রমাণ করাে;
f sin 19° + sin 41 + sin 83° = sin 23° + sin37° + sin799
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Answer: L.H.S = sin 19 + sin 41 + sin 83
= sin 41 + sin 19 + sin 83
= 2 x sin (19 + 41)/2 x cos (41 - 19)/2 + sin 83
= 2 x sin 30 x cos 11 + sin 83
= 2x 1/2 x cos 11 + sin 83
= cos 11 + sin 83
= sin (90 -79) + sin 83
= sin 79 + sin 83
R.H.S = sin 23 + sin 37 + sin 799
= sin 37 + sin 23 + sin 799
= 2 x sin (37+23)/2 x cos (37-23)/2 + sin (90 x 8 +79)
= 2 x sin 30 x cos 7 + sin 79
= 2 x 1/2 x cos 7 + sin 79
= cos 7 + sin 79
= sin (90 - 83) + sin 79
= sin 83 + sin 79
Therefore , L.H.S. = R.H.S (Proved)
Step-by-step explanation:
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