Question

the value of (1+tan32°)(1+tan13°)/(1+tan23°)(1+tan22°)=​

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)

⇒ $\frac{tan32+tan13}{1-tan32tan13}=tan45$  ∵tan(A+B)=$\frac{tanA+tanB}{1-tanAtanB}$

⇒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

Answer 2

Answer:

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)

⇒   ∵tan(A+B)=

⇒tan32+tan13=1-tan32tan13

⇒tan13+tan32+tan32tan13=1

similarly 22+23=45

⇒tan22+tan23+tan22tan23=1

substituting values in above equations

=1

Step-by-step explanation: