Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev

The document Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.
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Q.1. Evaluate:
Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
(iii) cos 48° − sin 42°
(iv) cosec 31° − sec 59°
Sol. 
Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
[∵ cos (90° - θ) = sin θ]
Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev

Q.2. Show that: 
(i) tan 48° tan 23° tan 42° tan 67° = 1
(ii) cos 38° cos 52° − sin 38° sin 52° = 0 
Sol. (i) LHS = tan 48° tan 23° tan 42° tan 67°
= tan 48° tan 23° tan (90° - 48°) tan (90° - 23°)
= tan 48° tan 23° cot 48° cot 23°
Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
(ii) LHS = cos 38° cos 52° - sin 38° sin 52°
= cos 38° cos (90° - 38°) - sin 38°sin (90° - 38°)
= cos 38° sin 38°- sin 38° cos 38° = 0 = RHS

Q.3. If tan 2A = cot (A − 18°), where 2A is an acute angle, find the value of A.
Sol. tan 2A = cot (A - 18°)
⇒ cot (90° - 2A) = cot (A - 18°)
[∵ cot (90° - θ) = tan θ]
⇒ 90° - 2A = A - 18°
Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
∴  ∠A = 36°

Q.4. If tan A = cot B, prove that A + B = 90°.
Sol. tan A = cot B
⇒ tan A = tan (90° - B)
[∵ tan (90° - θ) = cot θ]
⇒ A = 90° - B
⇒ A + B = 90°       Proved

Q.5. If sec 4A = cosec (A − 20°), where 4A is an acute angle, find the value of A.
Sol. sec 4A = cosec (A - 20°)
⇒ cosec (90° - 4A) = cosec (A - 20°) [cosec (90° - θ) = sec θ]
⇒ 90° - 4A = A - 20°
Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
∴ ∠A = 22º

Q.6. If A, B and C are interior angles of a triangle ABC, then show that

Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Sol. In ΔABC, A + B + C = 180° ⇒ B + C = 180° - A
Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev
Ex 8.3 NCERT Solutions- Introduction to Trigonometry Class 10 Notes | EduRev

Q.7. Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.
Sol. sin 67° + cos 75° = sin (90° - 23°) + cos (90° - 15°)
= cos 23° + sin 15°

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