Trigonometrical Ratios Class-9 Concise ICSE Mathematics Selina Solutions Chapter-22 . We provide step by step Solutions of Exercise / lesson-22 Trigonometrical Ratios for ICSE Class-9 Concise Selina Mathematics by R K Bansal.
Our Solutions contain all type Questions with Exe-22 A and Exe-22 B, to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics .
Trigonometrical Ratios Class-9 Concise ICSE Mathematics Selina Solutions Chapter-22
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Exercise 22 (A), Trigonometrical Ratios Class-9 Concise ICSE Mathematics Selina Solutions
Question 1
From the following figure, find the values of :
(i) sin A
(ii) cos A
(iii) cot A
(iv) sec C
(v) cosec C
(vi) tan C.
Answer
Question 2
Form the following figure, find the values of :
(i) cos B
(ii) tan C
(iii) sin2B + cos2B
(iv) sin B. cos C + cos B. sin C
Answer
Question 3
From the following figure, find the values of :
(i) cos A (ii) cosec A
(iii) tan2A – sec2A (iv) sin C
(v) sec C (vi) cot2 C – 1/sin² C
Answer
Question 4
From the following figure, find the values of :
(i) sin B (ii) tan C
(iii) sec2 B – tan2B (iv) sin2C + cos2C
Answer
Question 5
Given: sin A = 3/5 , find :
(i) tan A(ii) cos A
Answer
Question 6
From the following figure, find the values of :
(i) sin A
(ii) sec A
(iii) cos2 A + sin2A
Answer
Question 7
Given: cos A = 5/13
Evaluate: (i)( sin A – Cot A ) /2 Tan A (ii) cot A+ (1 / cos A)
Answer
Question 8
Given: sec A =29/11 , evaluate : sin A – 1/ Tan A
Answer
Question 9
Given: tan A =4/3 , find : cosecA/( cot A-sec A)
Answer
Question 10
Given: 4 cot A = 3 find;
(i) sin A
(ii) sec A
(iii) cosec2 A – cot2A.
Answer
Question 11
Given: cos A = 0.6; find all other trigonometrical ratios for angle A.
Answer
Question 12
In a right-angled triangle, it is given that A is an acute angle and tan A =. 5/12
find the value of :
(i) cos A(ii) sin A(iii) c(os A + sin A) / (cos A – Sin A)
Answer
Question 13
Given: sin θ =p/q
Find cos θ + sin θ in terms of p and q.
Answer
Question 14
If cos A =1/2 and sin B 1/ √2 = , find the value of : .
Tan A – Tan B / ( 1+tan A . Tan B)
Are angles A and B from the same triangle? Explain.
Answer
Question 15
If 5 cot θ = 12, find the value of : Cosec θ + sec θ
Answer
Question 16
If tan x = 1 1/3, find the value of : 4 sin2x – 3 cos2x + 2
Answer
Question 17
If cosec θ= √5, find the value of:
(i) 2 – sin2 θ- cos2 θ
(ii) ……….
Answer
Question 18
If sec A√2 = , find the value of :…………
Answer
Question 19
If cot = 1; find the value of: 5 tan2 + 2 sin2 – 3
Answer
Question 20
In the following figure:
AD BC, AC = 26 CD = 10, BC = 42,
DAC = x and B = y.
Find the value of :
(i) cot x
(ii) …………
(iii) ………….
Answer
Trigonometrical Ratios Class-9 Concise ICSE Mathematics Selina Solutions Exercise 22(B)
Question 1
From the following figure, find:
(i) y (ii) sin xo
(iii) (sec xo – tan xo) (sec xo + tan xo)
Answer
Question 2
Use the given figure to find:
(i) sin xo (ii) cos yo
(iii) 3 tan xo – 2 sin yo + 4 cos yo.
Answer
Question 3
In the diagram, given below, triangle ABC is right-angled at B and BD is perpendicular to AC. Find:
(i) cos DBC (ii) cot DBA
Answer
Question 4
In the given figure, triangle ABC is right-angled at B. D is the foot of the perpendicular from B to AC. Given that BC = 3 cm and AB = 4 cm. find:
(i) tan DBC
(ii) sin DBA
Answer
Question 5
In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC.
Answer
Question 6
In the figure given below, ABC is an isosceles triangle with BC = 8 cm and AB = AC = 5 cm. Find:
(i) sin B (ii) tan C
(iii) sin2 B + cos2B (iv) tan C – cot B
Answer
Question 7
In triangle ABC; ABC = 90o, CAB = xo, tan xo = and BC = 15 cm. Find the measures of AB and AC.
Answer
Question 8
Using the measurements given in the following figure:
(i) Find the value of sin and tan.
(ii) Write an expression for AD in terms of
Answer
Question 9
In the given figure;
BC = 15 cm and sin B =.
(i) Calculate the measure of AB and AC.
(ii) Now, if tan ADC = 1; calculate the measures of CD and AD.
Also, show that: tan2B – 1/cos² B = -1
Answer
Question 10
If sin A + cosec A = 2;
Find the value of sin2 A + cosec2 A.
Answer
Question 11
If tan A + cot A = 5;
Find the value of tan2 A + cot2 A.
Answer
Question 12
Given: 4 sin = 3 cos ; find the value of:
(i) sin (ii) cos
(iii) cot2 – cosec2.
(iv) 4 cos2– 3 sin2+ 2
Answer
Question 13
Given : 17 cos = 15;
Find the value of: tan + 2 sec.
Answer
Question 14
Given : 5 cos A – 12 sin A = 0; evaluate :
………….
Answer
Question 15
In the given figure; C = 90o and D is mid-point of AC. Find
(i) tan CAB / Tan CDB (ii) Tan ABC / Tan CDB
Answer
Question 16
If 3 cos A = 4 sin A, find the value of :
(i) cos A (ii) 3 – cot2 A + cosec2A.
Answer
Question 17
In triangle ABC, B = 90o and tan A = 0.75. If AC = 30 cm, find the lengths of AB and BC.
Answer
Question 18
In rhombus ABCD, diagonals AC and BD intersect each other at point O.
If cosine of angle CAB is 0.6 and OB = 8 cm, find the lengths of the the side and the diagonals of the rhombus.
Answer
Question 19
In triangle ABC, AB = AC = 15 cm and BC = 18 cm. Find:
(i) cos B (ii) sin C
(iii) tan2 B – sec2 B + 2
Answer
Question 20
In triangle ABC, AD is perpendicular to BC. sin B = 0.8, BD = 9 cm and tan C = 1. Find the length of AB, AD, AC and DC.
Answer
Question 21
Given q tan A = p, find the value of :
…………….
Answer
Question 22
If sin A = cos A, find the value of 2 tan2A – 2 sec2 A + 5.
Answer
Question 23
In rectangle ABCD, diagonal BD = 26 cm and cotangent of angle ABD = 1.5. Find the area and the perimeter of the rectangle ABCD.
Answer
Question 24
If 2 sin x = , evaluate.
(i) 4 sin3 x – 3 sin x.
(ii) 3 cos x – 4 cos3 x.
Answer
Question 25
If sin A = √3/2 and cos B = √3/2, find the value of : .
………………
Answer
Question 26
Use the information given in the following figure to evaluate:
……………. 6 cot y
Answer
Question 27
If sec A = √2 , find: ………….
Answer
Question 28
If 5 cos = 3, evaluate : …………
Answer
Question 29
If cosec A + sin A = 5,1/5 find the value of cosec2A + sin2A.
Answer
Question 30
If 5 cos = 6 sin ; evaluate:
(i) tan θ (ii) ………..
Answer
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