Question

prove That tan15+tan30+tan15.tan30=1

Answer 1

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

here A= 30, B= 15 

tan(45) = (tan30 + tan 15)/(1-tan30×tan15) 

and we know that tan(45) =1 

So, 1 = ( tan30 + tan 15)/(1-tan30×tan15) 

Taking denominator to the Right hand side 

(1-tan30×tan15) = ( tan30 + tan 15)

Hence, tan30 + tan 15+ tan30×tan15=1