CBSE Class 10 Mathematics Basic 2023: 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 $=\left(\frac{1}{\sin A}-\sin A\right)\left(\frac{1}{\cos A}-\cos A\right)$

   ½ mark

2. $=\frac{1-{\sin }^{2}A}{\sin A}\times \frac{1-{\cos }^{2}A}{\cos A}=\frac{{\cos }^{2}A{\sin }^{2}A}{\sin A\cos A}=\sin A\cos A$

   1 mark

3. $=\frac{\sin A\cos A}{{\sin }^{2}A+{\cos }^{2}A}$ [since ${\sin }^{2}A+{\cos }^{2}A=1$]

   ½ mark

4. Dividing numerator and denominator by $\sin A\cos A$: $=\frac{1}{\frac{\sin A}{\cos A}+\frac{\cos A}{\sin A}}=\frac{1}{\tan A+\cot A}=$ RHS

   1 mark

Answer: LHS = RHS, proved.

Revise the chapter

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