Home
Class 11
MATHS
Show that sin^2 5^0+sin^2 10^0+sin^2 15^...

Show that `sin^2 5^0+sin^2 10^0+sin^2 15^0++sin^2 90^0=9 1/2dot`

Text Solution

AI Generated Solution

To show that \( \sin^2 5^\circ + \sin^2 10^\circ + \sin^2 15^\circ + \ldots + \sin^2 90^\circ = \frac{19}{2} \), we will follow these steps: ### Step 1: Write the series We start with the left-hand side (LHS): \[ \text{LHS} = \sin^2 5^\circ + \sin^2 10^\circ + \sin^2 15^\circ + \ldots + \sin^2 90^\circ \] ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|482 Videos

Similar Questions

Explore conceptually related problems

Show that sin^(2)16^@+sin^(2)23^(@)+sin^(2)37^(0)+sin^(2)44^@=1+sin^(2)7^(0)+sin^(2)14^(@)

The value of the expression (1-4sin 10^0 sin 70^0)/(2sin 10^0 ) is- a.1/2 b. 1 c.2 d. none of these

Knowledge Check

  • The value of sin^2 5^@ + sin^2 10^@ + sin^2 15^@ + sin^2 20^@ + ... + sin^2 90^@ is:

    A
    7
    B
    8
    C
    9
    D
    `(19)/(2)`

  • Find the value of sin^(2)5^(@)+ sin^(2)10^(@)+ sin^(2)15^(@)+* * * +sin^(2)90^(@) .

    A
    8
    B
    9
    C
    `(17)/(2)`
    D
    `(19)/(2)`

  • The value of sin^(2)5^(@)+sin^(2)10^(@)+sin^(2)15^(@)+………+sin^(2)90^(@) is

    A
    `8 1/2`
    B
    `9 1/2`
    C
    `10 1/2`
    D
    `11 1/2`

    • Similar Questions

    Explore conceptually related problems

    If A+B+C = 180^0 , Prove that : sin^2 (A/2) + sin^2 (B/2) + sin^2 (C/2) =1-2 sin (A/2) sin (B/2) sin (C/2)

    sin ^ (2) 5 + sin ^ (2) 10 + sin ^ (2) 15 + ... + sin ^ (2) 180 =

    "Show that "sin^(2)16^(@)+sin^(2)23^(@)+sin^(2)37^(@)+sin^(2)44^(0)=1+sin^(2)7^(0)+sin^(2)14^(@)

    sin(2sin^(-1) 0.8)=

    " If "sin^(2)1^(0)*sin^(2)3^(0)*sin^(2)5^(0)......sin^(2)89^(0)=m^(n)." Then "|m-n|=

    Home
    Profile