Question

sin 20 sin 40 sin 60 sin 80=3/16

Answer 1

=sin(20) sin(40) sin (60) sin (80)=sin(60) sin(20) sin(40) sin (80)=√3/2 [sin(20) sin(40) sin(80)] -------------- (1) {since sin(60) = √3 /2}Taking sin(20) sin(40) sin(80)= sin (20) [ sin(40) sin (80) ]= sin (20) [sin (60-20) sin (60+20)]= sin (20) [sin^2 (60) - sin^2 (20)]= sin (20) [(√3/2)^2 - sin^2 (20)]= sin (20) [3/4 - sin^2 (20)]= 3/4 sin (20) - sin^3 (20)Taking LCM= 3sin (20) - 4sin^3 (20)/4= 1/4 [3sin (20) - 4sin^3 (20)]= 1/4 sin 3(20)= 1/4 sin (60)= 1/4 (√3/2)= √3/8 --------------------- (2)substitute equation (2) in equation (1)= (√3/2)(√3/8)= 3/16 ------------------------ RHS

Answer 2

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