Question

$prove \: that \\ \tan6 \tan42 \tan66 \tan78 = 1$

















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Answer 1

${\boxed{\boxed{\begin{array}{cc}\bf \:L.H.S = \rm \: tan \: {6}^{ \circ}.tan \: {42}^{ \circ} .tan \: {66}^{ \circ} .tan \: {78 } \\ \\ \rm = \frac{tan \: {54}^{ \circ} }{tan \: {54}^{ \circ} } \times tan \: {6}^{ \circ} .tan \: {42}^{ \circ} .tan \: {66}^{ \circ} .tan \: {78}^{ \circ} \\ \\ \rm = \frac{ \orange{(tan \: {6}^{ \circ} .tan \: {54}^{ \circ} .tan \:{66}^{ \circ} ) }(tan \: {42}^{ \circ} .tan \: {78}^{ \circ} )}{tan \: {54}^{ \circ} } \\ \\ \rm = \frac{ \orange{tan \: {6}^{ \circ} .tan({60}^{ \circ} - 6).tan({60}^{ \circ} + 6)}}{tan \: {54}^{ \circ} } \times tan \: {42}^{ \circ}.tan \: {78}^{ \circ} \\ \\ \orange{{\boxed{\begin{array}{cc}\bf \: we \: know \: that: \\ \\ \bf \: tan \: x.tan({60}^{ \circ} - x).tan({60}^{ \circ} + x) = tan \: 3x \\ \end{array}}}} \\ \\ \sf \: in \: the \: math \: \rm \: x = {6}^{ \circ} \\ \sf \: now \: apply \: this \\ \\ \rm = \frac{tan \: {(3 \times 6)}^{ \circ}.tan \: {42}^{ \circ} .tan \: {78}^{ \circ} }{tan \: {54}^{ \circ} } \\ \\ \rm = \frac{tan \: {18}^{ \circ}.tan \: {42}^{ \circ} .tan \: {78}^{ \circ} }{tan \: {54}^{ \circ} } \\ \\ \rm = \frac{tan \: {18}^{ \circ}.tan({60}^{ \circ} - 18).tan({60}^{ \circ} + 18 )}{tan \: {54}^{ \circ} } \\ \\ \rm = \frac{tan(3 \times 18){}^{ \circ} }{tan \: {54}^{ \circ} } \\ \\ \rm = \frac{ \cancel{tan \: {54}^{ \circ} }}{ \cancel{tan \: {54}^{ \circ}} } \\ \\ = 1 \\ \\ \bf = R.H.S\end{array}}}}$

Hence ___ (Proved)

________

Good noon... $\ddot\smile$

Jananor jonno thanks.

Jodi abar date change na hoi tahole, amar 1st exam

• DU → 1st October

R baki gulo

RU → 4th October

BUET exam er 10 din agei janabe.

BUET a to aibar 2 bar exam hobe

[preliminary + written]

others akhono kisui bole ni.

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Answer 2

Answer:

An anthropologist is a person engaged in the practice of anthropology. Anthropology is the study of aspects of humans within past and present societies. ... Linguistic anthropology studies how language affects social life, while economic anthropology studies human economic behavior.