Proof expression: cos ⁡ ( 80 ° ) ∗ sin ⁡ ( 70 ° ) ∗ cos ⁡ ( 60 ° ) ∗ sin ⁡ ( 50 ° ) = 1 16

Question

Proof expression:   cos  ⁡  (  80      °    )  ∗  sin  ⁡  (  70      °    )  ∗  cos  ⁡  (  60      °    )  ∗  sin  ⁡  (  50      °    )  =      1    16

Everett Mclaughlin · Accepted Answer

cos  ⁡  80      °    sin  ⁡  70      °    cos  ⁡  60      °    sin  ⁡  50      °    =            8      sin      ⁡              20                  ∘                    cos      ⁡              20                  ∘                    cos      ⁡              40                  ∘                    cos      ⁡              80                  ∘                            16      sin      ⁡              20                  ∘                      =  =            sin      ⁡              160                  ∘                            16      sin      ⁡              20                  ∘                      =      1    16

Proof expression: cos(80^@) sin(70^@) cos(60^@) sin(50^@)=1/16 I tried in different ways, but I always get sin(20^@) in expression, which I can't simplify. What is the fastest way to prove this?

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