Show that the following III — task. Maths CBSE Live product, Class 10 (2026-27).

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:

\frac{\cos θ}{1 + \sin θ} \times \frac{1 - \sin θ}{1 - \sin θ}

\frac{1 - \sin θ}{\cos θ}

\(sin^2\ \theta + cos^2\ \theta = 1\)

\(sin^2\ \theta - cos^2\ \theta =1\)

\frac{\cos θ (1 - \sin θ)}{1 - \sin^{2} θ}

\frac{\cos θ (1 - \sin θ)}{(1 + \sin θ) (1 - \sin θ)}

\frac{\cos θ (1 - \sin θ)}{\cos^{2} θ}

Did you find an error?

7. Show that the following III