NCERT Solutions for class 10th Maths Chapter 8 Introduction to Geometry

Exercise 8.1

Question 1. In AABC, right-angled at B, AB= 24 cm, BC= 7 cm. Determine :
(i) sin A, cos A (ii) sin C, cos C

Question 2. In given figure find tan P – cot R :

Question 3. If sin A = 3/4 calculate cos A and tan A.

Question 4. Given 15cotA=8, find sin A and sec A.

Question 5. Given sec0 = 13/12, calculate all other trigonometric ratios.

Question 6. If LA and LB are acute angles such that cosA = cos B, then show that LA = LB.

Note : Side opposite to any acute angle 0 in right triangle is always perpendicular

Question 7. If cot0 = 7/8 evaluate :

Question 8. If 3cotA = 4, check whether

Question 9. In triangle ABC, right-angled at B, if tan A= 1/root3, find the value of:

Question 10. In PQR, right-angled at Q, PR + QR= 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

Question 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= 12/5 for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin 0 = 3 for some angle 0.

Exercise 8.2

Question 1. Evaluate the following:

Question 2. Choose the correct option and justify your choice:

Note : A fraction having zero in its denominator is undefined.

Question 3. If tan(A+B)= root 3 and tan(A-B)= 1/root3 ;0Â° < A+B < 90,find A and B.

Question 4. State whether the following are true or false. Justify your answer.
(i) sin (A+ B) = sin A+ sin B.
(ii) The value of sin 0 increases as 0 increases.
(iii) The value of cos 0 increases as 0 increases.
(iv) sin 0 = cos 0 for all values of 0.
(v) cot A is not defined for A= 0Â°.

Exercise 8.3

Question 1. Evaluate

Question 2. Show that

Question 3. If tan2A =cot (A-18Â°), where 2A is an acute angle, find the value of A.

Question 4. If tan A= cot B, prove that A + B = 90Â°.

Question 5. If sec4A=cosec(A-20Â°), where 4A is an acute angle, find the value of A.

Question 6. If A, B, and C are interior angles of a triangle ABC, then show that

Question 7. Express sin 67Â° + cos 75Â° in terms of trigonometric ratios of angles between 0Â°and45Â°.

Exercise 8.4

Question 1. Express the trigonometric ratios sin A, sec A, and tan A in terms of cot A.

Question 2. Write all the other trigonometric ratios of LA in terms of sec A.

Question 3. Evaluate :

Question 4. Choose the correct option. Justify your choice.

Note: Writing the expression in terms of sin 0 and cos 0 makes it easier to solve.

Question 5. Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

Hint : Writing the expression in terms of sin 0 and cos 0

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