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(1+cos180/8) (1+cos540/8) (1+cos900/8) (1+cos1260/8) is equal to ??

(1+cos180/8) (1+cos540/8) (1+cos900/8) (1+cos1260/8) is equal to ??

Grade:10

1 Answers

shivamverma
19 Points
3 years ago
you can write (cos 900/8 )as (– cos 540/8)   
and cos 1260/8) as ( -cos 180/8)  
so  the original equation will become (1+cos 180/8) ( 1-cos 180/8) (1+cos 540/8)(1 -cos 540/8)  
upon further simplification you will get ( sin^2 180/8 )( sin^2 540/8)
then multiply and divide it by 4 
it will become ¼ x[( 2 . sin 180/8 . sin 540/8 )]^2
then use formulae of  2 sin A . sin B = cos [A-B]  –  cos [A+B]
and you will get ¼ x [cos 45-cos90]^2    
which is equal to ¼ x 1/2=1/8
 SO 1/8 IS THE REQUIRED ANSWER!!

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