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# X=sin70°sin50° y=cos60°cos80°,then xy?please give detailed explanation soon......

KESHAV
19 Points
3 years ago
Given  Sin 50 sin 70 . cos 60 cos 80

=cos(90-30) cos(90-10) . Sin 50 sin 70

Sin 10 Sin 30 Sin 50 sin 70

⇒ (1/ 2) Sin 10 Sin 50 sin 70   multiply and divide with 2 Cos 10

⇒ 2 Cos 10 Sin 10 Sin 50 sin 70 / (2 x 2 Cos 10)  { 2SinA Cos A = Sin2A }

⇒  Sin 20  Sin 50 sin 70 / ( 4 Cos 10)    multiply and divide with 2

⇒ 2 x Sin 20  Sin 50 sin (90 - 20) / (2 x 4 Cos 10

⇒ 2 Sin 20 Cos 20 Sin 50 / 8 Cos 10

⇒ Sin 40  Sin 50 / 8 Cos 10   { 2SinA Cos A = Sin2A }

Again multiply and divide with 2 .

⇒ 2 x Sin 40  Sin ( 90 - 40)  / 2 x 8 Cos 10.

⇒ 2 x Sin 40  Cos 40 / 2 x 8 Cos ( 90 - 80)

⇒ Sin 80  / 16 Sin 80 = 1 / 16.