Question

Prove that tan 44 × tan 46 =1

Answer 1

Answer:

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Answer 2

Tan 44 °   *  Tan 46°   = 1

Step-by-step explanation:

Tan 44 °   *  Tan 46°   = 1

LHS = Tan 44 °   *  Tan 46°

= (Sin44°/Cos44° ) * ( Sin 46°/Cos46°)

= Sin 44° * Sin 46 ° / Cos44° * Cos46°

Sinα = Cos(90° - α)

=> Sin 46° = Cos44°

   Sin 44° = Cos46°

= Sin 44° * Sin 46 ° / Sin46° * Sin44°

= 1

= RHS

QED

Another Method

LHS = Tan 44 °   *  Tan 46°

= (Tan 45° - 1°)(Tan 45° +  1°)

= (Tan45° - Tan1°)/(1 + Tan45° Tan1°)   *  (Tan45° + Tan1°)/(1 - Tan45° Tan1°)  

= (1 - Tan1°)/(1 + Tan1°)   *  (1  + Tan1°)/(1 - Tan1°)  

= 1

= RHS

QED

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