If $x cos\theta - sin\theta$ = 1, then $x^{2}+(1 + x^{2})sin\theta$ equals
If $x cos\theta - sin\theta$ = 1, then $x^{2}+(1 + x^{2})sin\theta$ equals
1). 2
2). 1
3). -1
4). 0
2 answers
x cos$\theta$ – sin$\theta$ = 1
=> x cos$\theta$ = 1 + sin$\theta$
=> x = $\frac{1}{cos$\theta$}$+$\frac{sin$\theta$}{cos$\theta$}$
=> x = sec$\theta$ + tan$\theta$ --- (i)
=> sec$\theta$ – tan$\theta$ = (ii)
From equation (i) + (ii),
$\therefore$ Expression = x2 – (1 + x2)sin$\theta$
= x2 – (1 + x2) × $\frac{x^{2}-1}{x^{2}+1}$
= x2 – x2 + 1 = 1.
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