CBSE Class 10 Mathematics Basic 2025: question 30

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. LHS $=\frac{\frac{\sin \theta }{\cos \theta }}{1-\frac{\cos \theta }{\sin \theta }}+\frac{\frac{\cos \theta }{\sin \theta }}{1-\frac{\sin \theta }{\cos \theta }}$

   ½ mark

2. $=\frac{{\sin }^2\theta }{\cos \theta (\sin \theta -\cos \theta )}+\frac{{\cos }^2\theta }{\sin \theta (\cos \theta -\sin \theta )}=\frac{{\sin }^2\theta }{\cos \theta (\sin \theta -\cos \theta )}-\frac{{\cos }^2\theta }{\sin \theta (\sin \theta -\cos \theta )}$

   ½ mark

3. $=\frac{{\sin }^3\theta -{\cos }^3\theta }{(\sin \theta -\cos \theta )\sin \theta \cos \theta }=\frac{(\sin \theta -\cos \theta )({\sin }^2\theta +\sin \theta \cos \theta +{\cos }^2\theta )}{(\sin \theta -\cos \theta )\sin \theta \cos \theta }$

   1 mark

4. $=\frac{1+\sin \theta \cos \theta }{\sin \theta \cos \theta }$ [using ${\sin }^2\theta +{\cos }^2\theta =1$]

   ½ mark

5. $=\frac{1}{\sin \theta \cos \theta }+1=\sec \theta \text{cosec}\theta +1=$ RHS. Hence proved.

   ½ mark

Answer: LHS simplifies to $\sec \theta \text{cosec}\theta +1$ = RHS

Revise the chapter

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