CBSE Class 10 Maths (Basic) 2025 · Paper 430(B) · Question 37

Introduction to Trigonometry 4 marks Medium

A teacher asked his students to draw a right triangle

A B C

with

A B = 8

cm,

∠ B = 9 0^{\circ}

and

B C = 15

cm. Based on the above, answer the following:

(i)Evaluate $(sin^{2} A - cos^{2} A)$ .[1]
(ii)Evaluate $(\frac{1}{cos ^{2} A} - \frac{1}{cot ^{2} A})$ .[1]
(iii)(a)Evaluate $\frac{2 tan A}{1 + tan ^{2} A}$ and prove that it is equal to $2 sin A cos A$ .[2]
(iii)(b) OREvaluate $\frac{tan ^{2} A - sec ^{2} A}{cot ^{2} A - csc ^{2} A}$ .[2]

Answer

(i)

\frac{161}{289}

; (ii)

1

; (iii)(a)

\frac{240}{289}

, which equals

2 sin A cos A = 2 \times \frac{15}{17} \times \frac{8}{17}

; hence proved; (iii)(b)

1

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