Question

sin theta + cos theta equal to root 2 then find the value of tan theta +cot theta

Answer 1

given sinx+cosx = √2

Squaring on both sides gives

(sinx+cosx)²=(√2)²

sin²x+cos²x+2sinxcosx =2

1+2sinxcosx=2 

sinxcox=1/2 .........................(i)

so tanx+cotx ⇒ (sinx/cosx ) + (cosx/sinx)
                      ⇒ (sin²x+cos²x)/sinxcox
                      ⇒1/sinxcox
from (i),we know sinxcox=1/2
           
                  ∴ So 1/sinxcox⇒2