Question

The value of (1+tan 32°)(1+tan 13°) (1+tan 23°) (1+tan 22°) is​

Answer 1

Answer:

1

Step-by-step explanation:

(1+tan32)(1+tan13)= 1+tan32+tan13+tan32tan13 ∵(1+a)(1+b)=1+a+ab

(1+tan23)(1+tan22)=1+tan22+tan23+tan22tan23

32+13=45

apply tan on both sides

tan(32+13)=tan(45)

⇒ \frac{tan32+tan13}{1-tan32tan13}=tan45

1−tan32tan13

tan32+tan13

=tan45 ∵tan(A+B)=\frac{tanA+tanB}{1-tanAtanB}

1−tanAtanB

tanA+tanB

⇒tan32+tan13=1-tan32tan13

⇒tan13+tan32+tan32tan13=1

similarly 22+23=45

⇒tan22+tan23+tan22tan23=1

substituting values in above equations

\frac{(1+tan32)(1+tan13)}{(1+tan23)(1+tan22)}=\frac{1+1}{1+1}

(1+tan23)(1+tan22)/(1+tan32)(1+tan13)

=

1+1/1+1

=1

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