CBSE Class 10 Mathematics Standard 2024: question 26

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Dividing numerator and denominator of the LHS by $\cos \theta$: LHS $=\frac{\tan \theta -1+\sec \theta }{\tan \theta +1-\sec \theta }$

   1 mark

2. Replace 1 in the denominator by ${\sec }^2\theta -{\tan }^2\theta$ [identity ${\sec }^2\theta -{\tan }^2\theta =1$]: $=\frac{\tan \theta -1+\sec \theta }{(\tan \theta -\sec \theta )+({\sec }^2\theta -{\tan }^2\theta )}$

   1 mark

3. Factorise the denominator: $(\tan \theta -\sec \theta )+(\sec \theta -\tan \theta )(\sec \theta +\tan \theta )=(\sec \theta -\tan \theta )(\tan \theta +\sec \theta -1)$, so LHS $=\frac{\tan \theta +\sec \theta -1}{(\sec \theta -\tan \theta )(\tan \theta +\sec \theta -1)}$

   ½ mark

4. Cancelling the common factor: LHS $=\frac{1}{\sec \theta -\tan \theta }=$ RHS. Hence proved.

   ½ mark

Answer: LHS = 1/(secθ − tanθ) = RHS, hence proved

Revise the chapter

• Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
• Topic: Proving Simple Trigonometric Identities