Question

(Tan 46 degree )( tan 14 degree ) - ( Tan 74 degree )( Tan 14 degree ) + ( Tan 74 degree )( Tan 46 Degree ).

Answer 1

Given :- Tan 46 degree )( tan 14 degree ) - ( Tan 74 degree )( Tan 14 degree ) + ( Tan 74 degree )( Tan 46 Degree ) ?

Solution :-

→ tan 46° * tan 14° - tan 74° * tan 14° + tan 74° * tan 46°

using :-

• tan A * tan B = 1 - [(tan A + tan B )/tan (A+B)] => In tan 46° * tan 14° and tan 74° * tan 46°
• tan A * tan B = [(tan A - tan B) / tan (A - B)] - 1 => In tan 74° * tan 14°

so,

→ 1 - {(tan 46° + tan 14°)/tan 60°} - [{(tan 74° - tan 14°)/tan 60°} - 1] + 1 - {(tan 74° + tan 46°)/tan 120°}

using :-

• tan 60° = √3
• tan 120° = - √3

then,

→ (1 + 1 + 1) + (- tan 46° - tan 14° - tan 74° + tan 14° + tan 74° + tan 46°) / √3

→ 3 + 0

→ 3 (Ans.)

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