Question

If tan A = 1/2 and
and cot B = 3
then what is the value of A+B​

Answer 1

Answer:

shown below

Step-by-step explanation:

tanA=1/2

cotB=3

according to trigonometry rule

tanB= 1/cotB

than

tan B= 1/3

apply the trigonometry formula of tan(A+B)

tan(A+B)= tanA+tanB/1- tanA*tanB

tan(A+B)=(1/2+1/3)/(1–1/3*1/2)- eq1

after solve the eq1 then get

tan(A+B)=(5/6)/(5/6)

both are cancel out then give

tan(A+B)=1 -eq2

after solution i move the tan in right hand side then tan is change to arctan(tan inverse)

A+B= arctan 1

arctan 1= Pi/4 or 45 degree

value of A+B= pi/4 or 45 degree

Answer 2

Answer:

tanA=1/2

cotB=3

according to trigonometry rule

tanB= 1/cotB

than

tan B= 1/3

apply the trigonometry formula of tan(A+B)

tan(A+B)= tanA+tanB/1- tanA*tanB

tan(A+B)=(1/2+1/3)/(1–1/3*1/2)- eq1

after solve the eq1 then get

tan(A+B)=(5/6)/(5/6)

both are cancel out then give

tan(A+B)=1 -eq2

after solution i move the tan in right hand side then tan is change to arctan(tan inverse)

A+B= arctan 1

arctan 1= Pi/4 or 45 degree

value of A+B= pi/4 or 45 degree