CBSE Class 10 Mathematics Chapter 8 Introduction to Trigonometry Multiple Choice Questions with Answers. MCQ Class 10 Maths Introduction to Trigonometry with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Mathematics Introduction to Trigonometry MCQs with Answers to know their preparation level.
Multiple Choice Questions - Set - 4
Question 1:
If x sin (90° – θ) cot (90° – θ) = cos (90° – θ), then x is equal to
(a) 0
(b) 1
(c) -1
(d) 2
Correct Answer – (B)
Question 2 :
f A + B = 90°, cot B = 3/4 then tan A is equal to:
(a) 5/3
(b) 1/3
(c) 3/4
(d) 1/4
Correct Answer – (C)
Question 3 :
If sin θ – cos θ = 0, then the value of (sin4 θ + cos4 θ) is
(a) 1
(b) 3/4
(c) 1/2
(d) 1/4
Correct Answer – (C)
sin θ – cos θ = 0
⇒ (sin θ – cos θ)² = 0
⇒ sin2²θ + cos²θ – 2 sin θ cos θ = 0
⇒ – 2 sin θ cos θ = – 1
⇒ 2 sin θ cos θ=1
⇒ sin θ cos θ = 1/2
⇒ sin²θ cos²θ = 1/4
sin4θ + cos4θ = sin4θ + cos4θ + 2 sin²θ cos²θ – 2 sin²θ cos²θ
= (sin²θ + cos² θ)² – 2 sin²θ cos²θ
= (1)² – 2 × 1/4 = 1 – 1/2 = 1/2
Question 4 :
If cosec A – cot A = —, then cosec A =
(a) 47/40
(b) 59/40
(c) 51/40
(d) 41/40
Correct Answer – (D)
cosec A – cot A = 4/5 ……(i)
Also cosec² A – cot² A = 1
⇒ (cosec A – cot A) (cosec A + cot A) = 1
⇒ (4/5)(cosec A + cot A) = 1
⇒ cosec A + cot A = 4/5 …(ii)
From (i) and (ii), cosec A = 41/40
Question 5 :
sin (90° – A) =
(a) sin A
(b) tan A
(c) cos A
(d) cosec A
Correct Answer – (C)
Question 6 :
If sec A + tan A = x, then tan A =
(a) 2/x
(b) 1/2x
(c) (x2-1)/2x
(d) 2x/(x2-1)
Correct Answer – (C)
secA + tanA = x … (i)
Also sec² A – tan² A = 1
⇒ (sec A – tan A) (sec A + tan A) = 1
⇒ x (sec A – tan A)
∴ sec A – tan A = 1/x ….. (ii)
Now, subtracting (ii) from (i), we have
tan A = (x2-1)/2x
Question 8 :
If sin x + cosec x = 2, then sin19x + cosec20x =
(a) 219
(b) 220
(c) 2
(d) 239
Correct Answer – (C)
⇒ sin x + (1/sinx) = 2
⇒ sin² x + 1 = 2 sin x
⇒ (sin x – 1)² = 0 => sin x = 1 => cosec x = 1
∴ sin19 x + cosec20 x = 1 + 1 = 2
Question 10 :
The value of the expression [cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ)] is
(a) -1
(b) 0
(c) 1
(d) 3/2
Correct Answer – (B)
= cosec {90° – (15° – θ)} – sec (15° – θ) – tan {90° – (35° – θ)} + cot (35° – θ)
= sec (15° – θ) – sec (15° – θ) – cot (35° – θ) + cot (35° – θ) = 0
- NCERT Solutions Class 10 Mathematics Introduction to Trigonometry : Exercise 8.1
- NCERT Solutions Class 10 Mathematics Introduction to Trigonometry : Exercise 8.2
- NCERT Solutions Class 10 Mathematics Introduction to Trigonometry : Exercise 8.3
- NCERT Solutions Class 10 Mathematics Introduction to Trigonometry : Exercise 8.4
