Advertisement Remove all ads

The Value of Sin25° + Sin210° + Sin215° + ... + Sin285° + Sin290° is - Mathematics

MCQ

The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is

Options

  • 7

  • 8

  • 9.5

  • 10

Advertisement Remove all ads

Solution

9.5

We have: 

\[ \sin^2 5^\circ + \sin^2 10^\circ + \sin^2 15^\circ + . . . + \sin^2 85^\circ + \sin^2 90^\circ\]

\[ = \sin^2 5^\circ + \sin^2 10^\circ + \sin^2 15^\circ + . . . + \sin^2 \left( 90^\circ - 10^\circ \right) + \sin^2 \left( 90^\circ - 5^\circ \right) + \sin^2 90^\circ\]

\[ = \sin^2 5^\circ + \sin^2 10^\circ + \sin^2 15^\circ + . . . + \cos^2 10^\circ + \cos^2 5^\circ + \sin^2 90^\circ\]

\[ = \left( \sin^2 5^\circ + \cos^2 5^\circ \right) + \left( \sin^2 10^\circ + \cos^2 10^\circ \right) + + \left( \sin^2 15^\circ + \cos^2 15^\circ \right)\]

\[ + \left( \sin^2 20^\circ + \cos^2 20^\circ \right) + \left( \sin^2 25^\circ + \cos^2 25^\circ \right) + \left( \sin^2 30^\circ + \cos^2 30^\circ \right) \]

\[ + \left( \sin^2 35^\circ + \cos^2 35^\circ \right) + \left( \sin^2 40^\circ + \cos^2 40^\circ \right) + \sin^2 45^\circ + \sin^2 90^\circ\]

\[ = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + \left( \frac{1}{\sqrt{2}} \right)^2 + \left( 1 \right)^2 \left[ \because \sin^2 \theta + \cos^2 \theta = 1 \right]\]

\[ = 8 + \frac{1}{2} + 1\]

\[ = 9 . 5\]

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 5 Trigonometric Functions
Q 16 | Page 42
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×