CBSE Class 10 Maths (Basic) 2024 · Paper 430/3/1 · Question 31(b)

Introduction to Trigonometry 3 marks Hard

cos A = \frac{5}{13}

, then verify that

\frac{cos A}{1 - tan A} + \frac{sin A}{1 - cot A} = cos A + sin A

Answer

With

sin A = \frac{12}{13}

tan A = \frac{12}{5}

and

cot A = \frac{5}{12}

: LHS

= - \frac{25}{91} + \frac{144}{91} = \frac{17}{13}

and RHS

= \frac{5}{13} + \frac{12}{13} = \frac{17}{13}

. Both sides equal

\frac{17}{13}

, so the result is verified.

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