Determine the value of the expression 5 sin 2 ⁡ A + 7 cos 2 ⁡ B if cos ⁡ A = − 2 3 and sin ⁡ B = 3 4

Question

Determine the value of the expression       5                  sin        2            ⁡      A        +      7                  cos        2            ⁡      B       if   cos  ⁡  A  =            −      2        3   and   sin  ⁡  B  =      3    4

Maffei2el · Accepted Answer

Using this trigononometric identity      cos          2        ⁡  θ  +      sin          2        ⁡  θ  =  1we get that      cos          2        ⁡  B  =  1  −      sin          2        ⁡  Bsimilary we can find       sin          2        ⁡  A, and then we just replace      5          1      −              cos                  2                    ⁡      A        +      7          1      −              sin                  2                    ⁡      B        =      5          1      −                        (                                    −              2                        3                    )                          2                      +      7          1      −                        (                      3            4                    )                          2

Determine the value of the expression (5)/(sin^2 A)+(7)/(cos^2 B) if cos A=-2/3 and sin B=3/4

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