Son 12'
sin 48° sin s4 =
Answers
Answer:
Let x = sin54 sin48 sin12
= (1/2) x sin 54 x ( 2 sin48 sin 12 )
We know, 2 sin A sin B =cos(A − B) − cos(A + B)
= 1/2 x sin54 x (cos36-cos60)
We know, sin( 90 - x ) = cos x and cos 60 = 1/2
=1/2 x cos36 x (cos36-1/2)
=1/2 x (cos36)² - 1/4 x cos36
We know, cos² x = 1 + cos 2x
=1/4 x (1+cos72) - 1/4 x cos36
=1/4 + (1/4)(cos72-cos36)
We know, cos A − cos B = - 2 sin (A + B/ 2) sin (A − B/ 2)
=1/4-1/2 x sin54 x sin18
We know, sin 90-x = cos x
=1/4-1/2 x cos36 x sin18
We multiply both sides with 8cos18
8cos18x = 8cos18 x (1/4-1/2 x cos36 x sin18)
8cos18x = 2cos18 - 4cos36 x sin18 x cos18
We know, sin 2 x =2 sin x cos x
8cos18x = 2cos18 - 2cos36 x sin36
8cos18x= 2cos18-sin72
8cos18x= 2cos18-cos18
8cos18x = cos18
Thus,
x=cos18/(8cos18)
=1/8
Answer:
1/18 is the answer of your questions