What are the steps to solve this limit lim x → 0 cos ⁡ ( x + π / 2 ) x ?

Question

What are the steps to solve this limit       lim          x      →      0                  cos      ⁡      (      x      +      π              /            2      )        x  ?

pelankp · Accepted Answer

cos  ⁡  (  x  +      π    2    )  =  −  sin  ⁡  (  x  )So             lim              x        →        0                            −        sin        ⁡        (        x        )            x        =    −    1

qtbabe9876a9 · Accepted Answer

lim          x      →      0            (                  cos        ⁡                  (          x          +                      π            2                    )                    x        )    =      lim          x      →      0            (    −                  sin        ⁡        (        x        )            x        )    =  −      (          lim              x        →        0                            sin        ⁡        (        x        )            x        )    =  −      (          lim              x        →        0                                      d                      d            x                          sin        ⁡        (        x        )                              d                      d            x                          x              )    =  −      (          lim              x        →        0                            cos        ⁡        (        x        )            1        )    =  −      (          lim              x        →        0              cos    ⁡    (    x    )    )    =  −      (    cos    ⁡    (    0    )    )    =−(1)=−1

What are the steps to solve this limit <munder> <mo movablelimits="true" form="prefix">lim

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