Find the value of ( ( tan 2 ⁡ 7 π 24 − tan 2 ⁡ π 24 ) : ( 1 − tan 2 ⁡ 7 π 24 tan 2 ⁡ π 24 ) ) 2

Question

Find the value of             (                  (            tan    2    ⁡            7      π        24    −      tan    2    ⁡      π    24              )        :            (        1  −      tan    2    ⁡            7      π        24        tan    2    ⁡      π    24              )                          )              2

last99erib · Accepted Answer

Hint:       A          2        −      B          2        =  (  A  −  B  )  (  A  +  B  )Further hint:Use the hint to rewrite the expression as             (                        tan          ⁡                      (            7            π                          /                        24            )                    −          tan          ⁡                      (            π                          /                        24            )                                    1          +          tan          ⁡                      (            7            π                          /                        24            )                    tan          ⁡                      (            π                          /                        24            )                              ⋅                        tan          ⁡                      (            7            π                          /                        24            )                    +          tan          ⁡                      (            π                          /                        24            )                                    1          −          tan          ⁡                      (            7            π                          /                        24            )                    tan          ⁡                      (            π                          /                        24            )                              )              2      Answer:The addition formula for   tan then gives you the answer:            (      tan      ⁡                                    6            π                    24                    tan      ⁡                                    8            π                    24                    )              2        =            (      tan      ⁡                        π          4                    tan      ⁡                        π          3                    )              2        =            (      1      ⋅              3            )              2        =  3

Find the value of ( ( tan 2 ⁡ 7 π 24 − tan 2...

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