PYQ - Trigonometric identities — task. Maths CBSE Live product, Class 10 (2025-26).

Using standard trigonometric identities show that :

\frac{\tan θ + \sec θ - 1}{\tan θ - \sec θ + 1} = \frac{1 + \sin θ}{\cos θ}

Proof:

LHS \(=\)

\frac{\tan θ + \sec θ - 1}{\tan θ - \sec θ + 1}

\(=\)

\(=\) RHS

Hence \(LHS = RHS\)

Answer variants:

\frac{(\tan θ + \sec θ) (1 + \tan θ - \sec θ)}{(\tan θ - \sec θ + 1)}

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

\frac{\tan θ + \sec θ + (\tan θ + \sec θ) (\tan θ - \sec θ)}{\tan θ - \sec θ + 1}

\frac{1 + \sin θ}{\cos θ}

\frac{\tan θ + \sec θ + (\tan^{2} θ - \sec^{2} θ)}{\tan θ - \sec θ + 1}

\frac{\tan θ + \sec θ - (\sec^{2} θ - \tan^{2} θ)}{\tan θ - \sec θ + 1}

\tan θ + \sec θ

Did you find an error?

4. PYQ - Trigonometric identities