Maharashtra BoardEnglish MediumSTD 10MathsQuestion Bank - P23 Marks
Question
Prove that $\frac{1+\sin B}{\cos B}+\frac{\cos B}{1+\sin B}=2 \sec B$
✓
Answer
$\text { L.H.S }=\frac{1+\sin B }{\cos B }+\frac{\cos B }{1+\sin B }$
$=\frac{(1+\sin B )^2+\cos ^2 B }{\cos B (1+\sin B )}$
$=\frac{1+2 \sin B +\sin ^2 B +\cos ^2 B }{\cos B (1+\sin B )} \quad \ldots \ldots\left[\because \cdot( a + b )^2= a ^2+2 a b+b^2\right]$
$=\frac{1+2 \sin B +1}{\cos B (1+\sin B )} \quad \ldots . .\left[\because \sin ^2 B +\cos ^2 B =1\right]$
$=\frac{2+2 \sin B }{\cos B (1+\sin B )}$
$=\frac{2(1+\sin B )}{\cos B (1+\sin B )}$
$=\frac{2}{\cos B }$
$=2 \sec B$
$=\text { R.H.S }$
$\therefore \frac{1+\sin B }{\cos B }+\frac{\cos B }{1+\sin B }=2 \sec B $
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