Exercise 8.3 (Revised) - Chapter 8 Introduction To Trigonometry class 10 ncert solutions Maths - SaraNextGen [2024-2025]

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On April 24, 2024, 11:35 AM

Exercise 8.3 (Revised) : Chapter 8 - Introduction To Trigonometry - Ncert Solutions class 10 - Maths

Question 1:

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

Answer:

We know that,

 will always be positive as we are adding two positive quantities.

Therefore, 

We know that, 

However, 

Therefore, 

Also,

Question 2:

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

Answer:

We know that,

Also, sin² A + cos² A = 1

sin² A = 1 − cos² A

tan²A + 1 = sec²A

tan²A = sec²A − 1

Question 3:

Evaluate

(i) 

(ii) sin25° cos65° + cos25° sin65°

Answer:

(i) 

 (As sin²A + cos²A = 1)

= 1

(ii) sin25° cos65° + cos25° sin65°

= sin²25° + cos²25°

= 1 (As sin²A + cos²A = 1)

Question 4:

Choose the correct option. Justify your choice.

(i) 9 sec² A − 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) 

(A) sec² A

(B) −1

(C) cot² A

(D) tan² A

Answer:

(i) 9 sec²A − 9 tan²A

= 9 (sec²A − tan²A)

= 9 (1) [As sec² A − tan² A = 1]

= 9

Hence, alternative (B) is correct.

(ii)

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

Hence, alternative (C) is correct.

(iii) (secA + tanA) (1 − sinA)

= cosA

Hence, alternative (D) is correct.

(iv) 

Hence, alternative (D) is correct.

Question 5:

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

Answer:

(i) 

(ii) 

(iii) 

= secθ cosec θ +

= R.H.S.

(iv) 

= R.H.S

(v) 

Using the identity cosec²  = 1 + cot² ,

L.H.S = 

= cosec A + cot A

= R.H.S

(vi) 

(vii) 

(viii) 

(ix) 

Hence, L.H.S = R.H.S

(x)