NCERT Solution for Class 10 Mathematics Chapter 8 - Trigonometry RR ACADEMY MEERUT MATHS BY RAKESH CHATURVEDI SIR

NCERT Solution for Class 10 Mathematics Chapter 8 - Trigonometry Page/Excercise 8.1

Question 1

In ABC right angled at B, AB = 24 cm, BC = 7 m. Determine

(i)  sin A, cos A
(ii)  sin C, cos C 

Solution 1

In ABC by applying Pythagoras theorem 
AC2 = AB2 + BC2
= (24)2 + (7)2
= 576 + 49
= 625
AC =  = 25 cm 

 

 

Question 2

Solution 2

Question 3

Solution 3

Question 4

Given 15 cot A = 8. Find sin A and sec A

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

NCERT Solution for Class 10 Mathematics Chapter 8 - Trigonometry Page/Excercise 8.2

Question 1

Solution 1

Question 2

Choose the correct option and justify your choice. 
 

(A).    sin60°    
(B).    cos60°    
(C).    tan60°
(D).    sin30° 
 
(A).    tan90°
(B).    1
(C).    sin45°
(D).    0


(iii).    sin2A = 2sinA is true when A = 

(A).    0°
(B).    30°
(C).    45°
(D).    60° 

 
(A).    cos60°
(B).    sin60°
(C).    tan60°
(D).    sin30°

Solution 2

 

Question 3

Solution 3

Question 4

State whether the following are true or false. Justify your answer.

(i).    sin(A + B) = sinA + sinB
(ii).   The value of sinθ increases as θ increases
(iii).  The value of cosθ increases as θ increases
(iv).  sinθ = cosθ for all values of θ
(v).   cotA is not defined for A = 0�

Solution 4

NCERT Solution for Class 10 Mathematics Chapter 8 - Trigonometry Page/Excercise 8.3

Question 1

Evaluate 

Solution 1

Question 2

Solution 2

Question 3

If tan 2A = cot (A - 18�), where 2A is an acute angle, find the value of A.

Solution 3

Given that

tan 2A = cot (A - 18�)

cot (90� - 2A) = cot (A -18�)
90� - 2A = A - 18�
108� = 3A
A = 36�

Question 4

If tan A = cot B, prove that A + B = 90�

Solution 4

Given that
tan A = cot B
tan A = tan (90� - B)
A = 90� - B
A + B = 90�

Question 5

If sec 4A = cosec (A - 20�), where 4A is an acute angle, find the value of A.

Solution 5

Given that
Sec 4A = cosec (A - 20�)
Cosec (90� - 4A) = cosec (A - 20�)
90� - 4A = A - 20�
110� = 5A
A = 22�

Question 6

Solution 6

Question 7

Express sin 67� + cos 75� in terms of trigonometric ratios of angles between 0� and 45�.

Solution 7

sin 67� + cos 75�
= sin (90� - 23�) + cos (90� - 15�)
= cos 23� + sin 15�

NCERT Solution for Class 10 Mathematics Chapter 8 - Trigonometry Page/Excercise 8.4

Question 1

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

Solution 1

We know that 

Question 2

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

Solution 2

We know that 

Question 3

Evaluate 

Solution 3

Question 4

Choose the correct option. Justify your choice.

(i).    9sec2 A - 9tan2 A = 
(A)    1
(B)    9
(C)    8
(D)    0 

(ii).    (1 + tanθ + secθ) (1 + cotθ - cosecθ)
(A)    0
(B)    1
(C)    2
(D)    -1


(iii).    (secA + tanA) (1 - sinA) =

(A)    secA
(B)    sinA
(C)    cosecA
(D)    cosA    


 
(A)    sec2A
(B)    -1
(C)    cot2A
(D)    tan2A

Solution 4

(i) 9sec2A - 9tan2A 
= 9(sec2A - tan2A)
= 9 (1)            [as sec2 A - tan2 A = 1]
= 9 

Hence alternative (B) is correct.


(ii) (1 + tanθ + secθ) (1 + cotθ - cosecθ) 
 
Hence alternative (C) is correct. 
(iii) (secA + tanA) (1 - sinA) 
 

(iv)

Question 5

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

Solution 5