Show that\(\frac{cos \theta}{1+sin \theta}=\frac{1-sin \theta}{cos \theta}\)
 
Proof:  
 
Consider, \(\frac{cos \theta}{1+sin \theta} = \)
 
\(=\)
 
\(=\)
 
By using identity,
 
\(=\)
 
\(=\)
 
\(LHS = RHS\)
 
Hence proved
Answer variants:
cosθ1+sinθ×1−sinθ1−sinθ
1−sinθcosθ
\(sin^2\ \theta + cos^2\ \theta = 1\)
\(sin^2\ \theta - cos^2\ \theta =1\)
cosθ(1−sinθ)1−sin2θ
cosθ(1−sinθ)(1+sinθ)(1−sinθ)
cosθ(1−sinθ)cos2θ