The value of sin25∘+sin210∘+sin215∘+.............. +sin285

Sail E0 Webinar

Question

The value of

{sin}^{2} 5^{\circ} + {sin}^{2} 10^{\circ} + {sin}^{2} 15^{\circ} +

..............

+ {sin}^{2} 85^{\circ} + {sin}^{2} 90^{\circ}

is equal to

Options:

A . 7

B . 8

C . 9

D . 192

Answer: Option D
:
D
Given expression is

{sin}^{2} 5^{\circ} + {sin}^{2} 10^{\circ} + {sin}^{2} 15^{\circ} + . . . . . . . . . . . . . . + {sin}^{2} 85^{\circ} + {sin}^{2} 90^{\circ}

.
We know that

sin 90^{\circ} = 1 or {sin}^{2} 90^{\circ} = 1

Similarly,

sin 45^{\circ} =

\frac{1}{\sqrt{2}}

or

{sin}^{2} 45^{\circ} = \frac{1}{2}

and the angles are in A.P. of 18 terms. We also know that

{sin}^{2} 85^{\circ} = [sin (90^{\circ} - 5^{\circ})]^{2} = {cos}^{2} 5^{\circ}

.
Therefore from the complementary rule, we find

{sin}^{2} 5^{\circ} + {sin}^{2} 85^{\circ} = {sin}^{2} 5^{\circ} + {cos}^{2} 5^{\circ} = 1

Therefore,

{sin}^{2} 5^{\circ} + {sin}^{2} 10^{\circ} + {sin}^{2} 15^{\circ} + . . . . . . . . . . . . . + {sin}^{2} 85^{\circ} + {sin}^{2} 90^{\circ}

= (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) + 1 + \frac{1}{2} = 9 \frac{1}{2}

.

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. If secθ = 54, then tan θ2 = ....

Question 2. If A + B = 225∘, then cotA1+cotA. cotB1+cotB =....

Question 3. If acos3α+3acosαsin2α=m and asin3α+3acos2αsinα=n, Then (m+n)23+(m−n)23 is e....If acos3α+3acosαsin2α=m and asin3α+3acos2αsinα=n, Then (m+n)23+(m−n)23 is equal to

Question 4. Tan α+2tan 2α+4tan 4α+8cot 8α= [IIT 1988; MP PET 1991]....

Question 5. If sin A = 45 and cos B = - 1213, where A and B lie in first and third quadrant respectively, then cos(A + B....in first and third quadrant respectively, then cos(A + B) =

Question 6. Cot215∘−1cot215∘+1 = ....

Question 7. The minimum value of 3sinθ+4cosθ is ....

Question 8. If 3π4<α<π, then √cosec2α+2cotα is equal to....

Question 9. If cos(θ−α) = a, sin(θ−β) = b, then cos2(α−β) + 2ab sin(α....sin(θ−β) = b, then cos2(α−β) + 2ab sin(α−β) is equal to

Question 10. If cos6α+sin6α+K sin22α=1, then K=....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0