Question

If 2tan = 2 tan, prove that tan( − ) = sin2 5−cos 2​

Answer 1

tan(α−β)

=1+tanαtanβtanα−tanβ

=1+23tan2β23tanβ−tanβ×cos2βcos2β

=4cos2β+6sin2βsin2β

=4+(1−cos2β)sin2β

=5−cos2βsin2β

tan(α−β)

=

1+tanαtanβ

tanα−tanβ

= 1+ 23 tan 2 β23 tanβ−tanβ

× cos 2 βcos 2 β

= 4cos 2 β+6sin 2 βsin2β

= 4+(1−cos2β)

sin2β

= 5−cos2

βsin2β

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Answer 2

$\huge\bold{AñSwEr}$

tan(α−β)= 1+tanαtanβtanα−tanβ

= 1+23tan2β23tanβ−tanβ×cos2βcos2β

= 4cos2β+6sin2βsin2β

= 4+(1−cos2β)sin2β

= 5−cos2βsin2β

tan(α−β) = 1+tanαtanβ

1+tanαtanβ tanα−tanβ

= 1+ 23 tan 2 β23 tanβ−tanβ × cos 2 βcos 2 β

= 4+(1−cos2β) sin2β

= 5−cos2

βsin2β

❥ Mɪᴢᴢ_Iɴɴᴏᴄᴇɴᴛ❦࿐