If 1 + sin θ =x cos θ , then tan θ is __
A
(x2+1)/x
B
(x2-1)/x
C
(x2+1)/2x
D
(x2-1)/2x
Correct Answer: (x2-1)/2x
1 + sin@ = xcos@Or, 1 + sin@/cos@ = xOr, 1/cos@ + sin@/cos = xOr, sec@ + tan@ = x...(i)We know, (Sec@ + tan@)(sec@ - tan@) = 1 Or, x(sec@ - tan@) = 1 Or, sec@ - tan@) = 1/x...(ii) (i) - (ii)Sec@ + tan@ - (sec@ - tan) = x - 1/xOr, Sec@ + tan@ - sec@ + tan@ = (xx - 1)/xOr, 2tan@ = (xx - 1)/x Tan@ = (xx - 1)/2x (Ans)