Prove taht (1+tan21)(1+tan28)(1+tan24)(1+tan17)=4

1.	Prove taht (1+tan21)(1+tan28)(1+tan24)(1+tan17)=4
Answer» tan 45 = tan ( 32 + 13) = (tan 32 + tan 13)/( 1- tan 32 tan 13) Therefore tan 32 + tan 13 = tan(45)( 1 - tan32 tan 13) = 1 - tan32 tan13 ..................... since tan 45 = 1 and tan 32 + tan 13 + tan 32 tan 13 = 1 Similarly tan 23 + tan 22 + tan 23 tan 22 = 1 Now (1+Tan32°)(1+tan13°)(1+tan23°)(1+tan22°) = ( 1+Tan32° + tan13° + tan32 tan 12)(1+tan23° + tan 22 + tan 23 tan 22) = ( 1 + 1 )(1 + 1) = 4

Answer»

tan 45 = tan ( 32 + 13)

= (tan 32 + tan 13)/( 1- tan 32 tan 13)

Therefore tan 32 + tan 13

= tan(45)( 1 - tan32 tan 13)

= 1 - tan32 tan13 ..................... since tan 45 = 1

and tan 32 + tan 13 + tan 32 tan 13 = 1

Similarly tan 23 + tan 22 + tan 23 tan 22 = 1

Now (1+Tan32°)(1+tan13°)(1+tan23°)(1+tan22°)

= ( 1+Tan32° + tan13° + tan32 tan 12)(1+tan23° + tan 22 + tan 23 tan 22)

= ( 1 + 1 )(1 + 1)

= 4

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Prove taht (1+tan21)(1+tan28)(1+tan24)(1+tan17)=4

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