Verify Trigonometric Identities 1 / sin ⁡ 50 ∘ + √ 3 / cos ⁡ 50 ∘ = 4

Question

Verify Trigonometric Identities  1      /    sin  ⁡      50    ∘    +      √    3      /    cos  ⁡      50    ∘    =  4

Gallichi5mtwt · Accepted Answer

LHS   (  cos  ⁡  50  +      √    3  sin  ⁡  50  )      /    sin  ⁡  50  cos  ⁡  50  (  2  cos  ⁡  50  +  2      √    3  sin  ⁡  50  )      /    2  sin  ⁡  50  cos  ⁡  50  (  2  cos  ⁡  50  +  2      √    3  sin  ⁡  50  )      /    (  sin  ⁡  100  )            2      cos      ⁡      50      +      2              2            sin      ⁡      50              sin      ⁡      100        =  4  ×                    1        2            cos      ⁡      50      +                        3                2            sin      ⁡      50              sin      ⁡      80        =  4  ×            sin      ⁡      30      cos      ⁡      50      +      cos      ⁡      30      sin      ⁡      50              sin      ⁡      80        =  4  ×            sin      ⁡      80              sin      ⁡      80      =4

Oberhangaps5z · Accepted Answer

1                      sin            ⁡                          50              ∘                                      +                              3                                cos            ⁡                          50              ∘                                      =        2                  (                                    1                              /                            2                                      sin              ⁡                              50                ∘                                              +                                                    3                                            /                            2                                      cos              ⁡                              50                ∘                                              )                =        2                  (                                    sin              ⁡                              30                ∘                                                    sin              ⁡                              50                ∘                                              +                                    cos              ⁡                              30                ∘                                                    cos              ⁡                              50                ∘                                              )                                    =                                    2        ⋅                              sin            ⁡                          30              ∘                        cos            ⁡                          50              ∘                        +            cos            ⁡                          30              ∘                        sin            ⁡                          30              ∘                                            sin            ⁡                          50              ∘                        cos            ⁡                          50              ∘                                      =        4        ⋅                              sin            ⁡            (                          30              ∘                        +                          50              ∘                        )                                2            sin            ⁡                          50              ∘                        cos            ⁡                          50              ∘                                                          =                                    4        ⋅                              sin            ⁡            (                          30              ∘                        +                          50              ∘                        )                                sin            ⁡            (            2            ⋅                          50              ∘                        )                          =        4        ⋅                              sin            ⁡                          80              ∘                                            sin            ⁡                          100              ∘                                          Now recall why   sin  ⁡      80    ∘    =  sin  ⁡      100    ∘

Verify Trigonometric Identities 1 <mrow class="MJX-TeXAtom-ORD"> / </mrow> sin

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