How to prove this? lim h → 0 sin ⁡ ( θ + h ) − sin ⁡ ( θ ) cos ⁡ ( θ + h ) − cos ⁡ ( θ ) = − 1 tan ⁡ ( θ )

Question

How to prove this?      lim          h      →      0                  sin      ⁡      (      θ      +      h      )      −      sin      ⁡      (      θ      )              cos      ⁡      (      θ      +      h      )      −      cos      ⁡      (      θ      )        =  −      1          tan      ⁡      (      θ      )

Schetterai · Accepted Answer

Hint:                              lim                      h            →            0                                                sin            ⁡            (            θ            +            h            )            −            sin            ⁡            (            θ            )                                cos            ⁡            (            θ            +            h            )            −            cos            ⁡            (            θ            )                                              =                  lim                      h            →            0                                                              sin              ⁡              (              θ              +              h              )              −              sin              ⁡              (              θ              )                        h                                              cos              ⁡              (              θ              +              h              )              −              cos              ⁡              (              θ              )                        h                                                            =                                            sin              ′                        ⁡            (            θ            )                                              cos              ′                        ⁡            (            θ            )

hawatajwizp · Accepted Answer

Hint :      lim          h      →      0                  f      (      a      +      h      )      −      f      (      a      )        h    =      f    ′    (  a  )

How to prove this? <munder> <mo movablelimits="true" form="prefix">lim <mrow class="

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