Introduction to Trigonometry – Exercise 8.4 – Class 10

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

8.png

Solution:

We know that,

1.png


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

Solution:

We know that

2.png


3. Evaluate (i) (sin263° + sin227°)/(cos217°+cos273°)

(ii) sin25° cos65° + cos25° sin65° 

Solution:

(i)

3.png

4.png

(ii)sin25° cos65° + cos25° sin65° 

= (sin25°){cos(90°-25°)} + cos25°{sin(90°-25°)}

= (sin25°)(sin25°)+(cos25°)(cos25°)

= (sin225°) + cos225°

= 1


4. Choose the correct option. Justify your choice.

(i) 9 sec2A − 9 tan2 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)(1+tan2A)/(1+cot2A) =

(A) sec2A

(B) -1

© cot2A

(d) tan2A

Solution:

(i) 9 sec2 A − 9 tan2 A

= 9 (sec2 A – tan2 A)

= 9 (1)  [Because  sec2 A − tan2 A = 1]

= 9

(B) is correct.

 

(ii) (1 + tan θ + sec θ) (1 + cot θ − cosec θ)

5

(C) is correct.

 

(iii)

6.png= cosA

(D) is correct.

(iv)

7.png

(D) is correct.

 


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

8.png

Solution:

9.png

10

Solution:

12

(iii)

13.png

Solution:

14.png

= secθ cosec θ + 1 = R.H.S.

 

(iv)

15.png

Solution:

16.png

 

(v)

17.png

solution:

18.png

= cosec A + cot A = R.H.S

(vi)

19

Solution:

20


 

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9 thoughts on “Introduction to Trigonometry – Exercise 8.4 – Class 10

  1. Pingback: X- Table of Contents – Breath Math

  2. Very nice post! I have seen first in WordPress. Can you please tell me how you write mathematical numbers in your blog because its difficult to show powers or exponents what app you used. Can you please tell me.

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