Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev

The document Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

Q.1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
Sol.  From trigonometric identity,
cosec2 A - cot2 A = 1, we get
cosec2 A = 1 + cot2A
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Again from trigonometric identity
sec2 A - tan2 A = 1
⇒ sec2 A = 1+ tan2 A
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Since  Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev

Q.2. Write all the other trigonometric ratios of ∠A in terms of sec A.
Sol. Since sin2 A+ cos2 A = 1,
therefore sin2 A = 1 - cos2A
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev

Q.3. Evaluate:

Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
(ii) sin 25° cos 65° + cos 25° sin 65°
Sol.
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
(ii) sin 25° cos 65° + cos 25° sin 65°
= sin 25° cos (90° - 25°) + cos 25° sin (90° -25°)
= sin 25° sin 25° + cos 25° cos 25°
= sin2 25° + cos2 25° = 1

Q.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) (sec A + tan A) (1 − sin A) = 
(A) sec A 
(B) sin A 
(C) cosec A 
(D) cos A

Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
(A) sec2 A
(B) −1
(C) cot2 A
(D) tan2 A

Sol. (i) Since, 9 sec2 A − 9 tan2 A = 9 (sec2 A − tan2 A)
= 9 x 1 = 9  
∴ The option (B) is correct.
(ii)  (1 + tan θ + sec θ) (1 + cot θ − cosec θ)
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
(iii) (sec A + tan A) (1 - sin A)
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev

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

Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
[Hint: Write the expression in terms of sin θ and cos θ]

Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
[Hint: Simplify LHS and RHS separately]

Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev  using the identity cosec2 A = 1 + cot2 A.

Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
(viii) (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
[Hint: Simplify LHS and RHS separately]
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Sol. (i) LHS = (cosec θ - cot θ)
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.4 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev

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