SSC CHSL 6 Dec 2015 Shift 1 Paper

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Question : 127 of 200

Marks: +1, -0

The value of the expression

Sin ^2 1° + Sin^ 2 11°+ Sin ^2 21 °

+ Sin^ 2 31 ° + Sin ^2 41° + Sin ^4 5 2 °

+Sin^ 2 49 °+ Sin^ 2 59° + Sin^2 69°

+ Sin ^2 79 °+ Sin ^2 89°

5
$5 1/2$
0
$4 1/2$

Solution:

Expression :

Sin ^2 1° + Sin^ 2 11°+ Sin ^2 21 °

+ Sin^ 2 31 ° + Sin ^2 41° + Sin ^4 5 2 °

+Sin^ 2 49 °+ Sin^ 2 59° + Sin^2 69°

+ Sin ^2 79 °+ Sin ^2 89°

=

(Sin ^21 ° + Sin ^2 89°)+ (Sin ^2 11 ° + Sin ^2 79°)

(Sin ^2 21° + Sin ^2 69°)+ (Sin^ 2 31° + Sin ^2 59 °)

+(Sin ^2 41° +Sin ^2 49°) + (Sin ^2 45 °)

=

[Sin ^2 1 °+ Sin ^2(90 °− 1 °)] +

[Sin ^2 11 ° + Sin^ 2(90 ° − 11 °)] +

[Sin^ 2 21°+ Sin^ 2(90 ° − 21°)]+

[Sin ^2 31 ° + Sin ^2(90° − 31 °)]

+ [Sin ^2 41° + Sin^2(90°− 41° )]

+ [Sin^2 45° ]

Using,

sin(90 ° − θ) = cos θ

(Sin ^2 1° + Cos^2 1 °) + (Sin^ 2 11°+ Cos^ 2 11°)

+ (Sin ^2 21° + Cos^ 2 21°)

+ (Sin ^2 31 °+ Cos ^2 31°)+ (Sin^ 2 41° + Cos ^2 41 °)

+ (Sin ^2 45 °)

Using,

sin^2 θ + cos^ 2 θ = 1

=

(1 + 1 + 1 + 1 + 1) +(1/√2)^2

=

5 + 1/2 = 5 1/2

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