In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine
(i) sin A, cos A
(ii) sin C, cos C
Answer :
Applying Pythagoras theorem for ΔABC, we obtain
AC^{2} = AB^{2} + BC^{2}
= (24 cm)^{2} + (7 cm)^{2}
= (576 + 49) cm^{2}
= 625 cm^{2}
∴ AC = cm = 25 cm
(i) sin A =
cos A =
(ii)
sin C =
cos C =
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In the given figure find tan P - cot R
Answer :
Applying Pythagoras theorem for ΔPQR, we obtain
PR^{2} = PQ^{2} + QR^{2}
(13 cm)^{2} = (12 cm)^{2} + QR^{2}
169 cm^{2} = 144 cm^{2} + QR^{2}
25 cm^{2} = QR^{2}
QR = 5 cm
tan P - cot R =
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If sin A =, calculate cos A and tan A.
Answer :
Given 15 cot A = 8. Find sin A and sec A
Answer :
Given sec θ =, calculate all other trigonometric ratios.
Answer :
If ∠ A and ∠ B are acute angles such that cos A = cos B, then show that
∠ A = ∠ B.
Answer :
If cot θ =, evaluate
(i) (ii) cot^{2} θ
Answer :
If 3 cot A = 4, Check whether
Answer :
In ΔABC, right angled at B. If, find the value of
(i) sin A cos C + cos A sin C
(ii) cos A cos C - sin A sin C
Answer :
In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
Answer :
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 =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 θ =, for some angle θ
Answer :
Evaluate the following
(i) sin60° cos30° + sin30° cos 60°
(ii) 2tan^{2}45° + cos^{2}30° - sin^{2}60°
(iii)
(iv)
(v)
Answer :
Choose the correct option and justify your choice.
(i)
(A). sin60°
(B). cos60°
(C). tan60°
(D). sin30°
(ii)
(A). tan90°
(B). 1
(C). sin45°
(D). 0
(iii) sin2A = 2sinA is true when A =
(A). 0°
(B). 30°
(C). 45°
(D). 60°
(iv)
(A). cos60°
(B). sin60°
(C). tan60°
(D). sin30°
Answer :
If and;
0° < A + B ≤90°, A > B find A and B.
Answer :
State whether the following are true or false. Justify your answer.
(i) sin(A + B) = sin A + sin B
(ii) The value of sinÃŽÂ¸increases as ÃŽÂ¸increases
(iii) The value of cos ÃŽÂ¸increases as ÃŽÂ¸increases
(iv) sinÃŽÂ¸= cos ÃŽÂ¸ for all values of ÃŽÂ¸
(v) cot A is not defined for A = 0°
Answer :
Evaluate
(I)
(II)
(III) cos 48° - sin 42°
(IV)cosec 31° - sec 59°
Answer :
Show that
(I) tan 48° tan 23° tan 42° tan 67° = 1
(II)cos 38° cos 52° - sin 38° sin 52° = 0
Answer :
If tan 2A = cot (A- 18°), where 2A is an acute angle, find the value of A.
Answer :
If tan A = cot B, prove that A + B = 90°
Answer :
If sec 4A = cosec (A- 20°), where 4A is an acute angle, find the value of A.
Answer :
If A, Band C are interior angles of a triangle ABC then show that
Answer :
Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.
Answer :
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
Answer :
Write all the other trigonometric ratios of ∠ A in terms of sec A.
Answer :
Evaluate
(i)
(ii) sin25° cos65° + cos25° sin65°
Answer :
Choose the correct option. Justify your choice.
(i) 9 sec^{2} A - 9 tan^{2} A =
(A) 1
(B) 9
(C) 8
(D) 0
(ii) (1 + tan θ + sec θ) (1 + cot θ - cosec θ)
(A) 0
(B) 1
(C) 2
(D) - 1
(iii) (secA + tanA) (1 - sinA) =
(A) secA
(B) sinA
(C) cosecA
(D) cosA
(iv)
(A) sec^{2} A
(B) - 1
(C) cot^{2} A
(D) tan^{2} A
Answer :
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
Answer :
Maths : CBSE NCERT Exercise Solutions for Class 10th for Introduction to Trigonometry ( Exercise 8.1, 8.2, 8.3, 8.4 ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.
Exercise 8.1 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Question 5 |
Question 6 |
Question 7 |
Question 8 |
Question 9 |
Question 10 |
Question 11 |
Exercise 8.2 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Exercise 8.3 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Question 5 |
Question 6 |
Question 7 |
Exercise 8.4 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Question 5 |