Question

If A+B+C=180 & Sinc=1 then prove tanA.tanB=1

Answer 1

Sin C = 1, therefore​ C = 90'.
Now,
A+B+90 = 180
A+B = 90
A = 90-B ---(1)

tan A x tan B = 1
tan (90-B) x tan B = 1
cot B x tan B = 1

Hence, proved.

Answer 2

Answer:

if sinc=1 then c=90'

Step-by-step explanation:

A+B+C=180

THEN A+B=90. (C=90)

A=90-B

tanA =tan(90-B)

now l. h. s = tanA. tanb

= tan(90-B) . tanB

= cotB. tanB

= 1. (proved)