Correct Option: B

x cosθ – sinθ = 1
⇒ x cosθ = 1 + sinθ

⇒ x =		1	+	sin θ
		cos θ		cos θ

⇒ x = secθ + tanθ --- (i)
∵ sec²θ – tan²θ = 1
⇒ (secθ + tanθ) (secθ – tanθ) =1

⇒ secθ – tanθ =	1	(ii)
	x

From equation (i) + (ii),

2secθ = x +		1	=	x² + 1
		x		x

⇒ secθ =	x² + 1
	2x

From equation (i) – (ii),

2tanθ = x –		1	=	x² - 1
		x		x

∴ tanθ =	x² - 1
	2x

∴ sinθ =	tanθ
	secθ

=		x² - 1	×	2x	=	x² - 1
		2x		x² + 1		x² + 1

∴ Expression = x² – (1 + x² ) sinθ

= x² - (1 + x²) ×	x² - 1	= x² - x² + 1 = 1
	x² + 1

Note : In the original equation x² + (1 + x² ) sinθ has been given that seems incorrect