Class 10, Maths, Chapter 8, Exercise 8.1, Solutions
Q.1 In Δ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine:
(i) sin A, cos A
(ii) sin C, cos C
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Q.2. In Figure, find tan P – cot R.
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Q.3. If sin A = $\frac{3}{4}$,calculate cos A and tan A.
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Q.4. Given 15 cot A = 8, find sin A and sec A.
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Q.5. Given sec θ = $\frac{13}{12}$, calculate all other trigonometric ratios.
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Q.6. If ∠ A and ∠ B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.
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Q.7. If cot θ = $\frac{7}{8}$, evaluate:
(i) $\frac{(1+\sin \,\,\theta )(1-\sin \,\,\theta )}{(1+\cos \,\,\theta )\,\,(1-\cos \,\,\theta )}$
(ii) cot2 θ
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Q.8. If 3 cot A = 4, check whether $\frac{1-{{\tan }^{2}}A}{1+{{\tan }^{2}}A}={{\cos }^{2}}A-{{\sin }^{2}}A$ or not.
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Q.9. In triangle ABC, right angled at B, if tan A = $\frac{1}{\sqrt{3}}$ find the value of:
(i) sin A cos C + cos A sin C
(ii) cos A cos C – sin A sin C
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Q.10. In Δ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
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Q.11. State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) sec A = $\frac{12}{5}$ for some value of angle A.
(iii) is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin θ = $\frac{4}{3}$ for some angle θ.
Ans: (i) False because sides of a right triangle may have any length, so tan A may have any value.
(ii) True, Hypotenuse is longest. Therefore, sec A is always greater than 1.
sec A $=\frac{12}{6}=\frac{H}{B}$
(iii) False, the abbreviation of cos A is not cosecant A.
Explanation: The abbreviation of cos A is cosin A and abbreviation of cosec A is cosecant A.
cos A → cosin A
cosec A → cosecant A
(iv) False as cot A is not the product of ‘cot’ and A. ‘cot’ separated from ‘A’ has no meaning.
