The value of the expression: sin21° + sin211° + sin221° + sin231° + sin241° + sin245° + sin249° + sin259° + sin269° + sin279° + sin289° is?

sin21° + sin211° + sin221° + sin231° + sin241° + sin245° + sin249° + sin259° + sin269° + sin279° + sin289° = (sin21° + sin289°) + (sin211° + sin279°) + (sin221° + sin269°) + (sin231° + sin259°) + (sin241° + sin249°) + sin245° = 1 + 1 + 1 + 1 + 1 + 12 [sin2A + sin2B = 1. If, A + B = 90°] = 512

This question belongs to Arithmetic Ability Trigonometry

Trigonometry

The value of the expression: sin²1° + sin²11° + sin²21° + sin²31° + sin²41° + sin²45° + sin²49° + sin²59° + sin²69° + sin²79° + sin²89° is?

A) 0 B) $${\text{5}}\frac{1}{2}$$ C) $${\text{4}}\frac{1}{2}$$ D) 5

Answer & Solution

Correct Answer: Option B

sin²1° + sin²11° + sin²21° + sin²31° + sin²41° + sin²45° + sin²49° + sin²59° + sin²69° + sin²79° + sin²89°
= (sin²1° + sin²89°) + (sin²11° + sin²79°) + (sin²21° + sin²69°) + (sin²31° + sin²59°) + (sin²41° + sin²49°) + sin²45°
= 1 + 1 + 1 + 1 + 1 + $$\frac{1}{2}$$ [sin²A + sin²B = 1. If, A + B = 90°]
= $$5\frac{1}{2}$$

Question posted by Examveda

Community

Join the Discussion

Join the discussion

No comments yet Be the first to discuss this question.

Keep Learning