Class 11th Maths – RD Sharma Chapter 5 : trigonometric Functions Multiple Choice Questions (MCQs Solutions
Mark the correct alternative in each of the following:
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If tan x = x − 1/4x , then sec x − tan x is equal to
(a) −2x , 1/2x
(b) −1/2x , 2x
(c) 2x
(d) 2x , 1/2x Watch Solution -
If sec x = x + 1/4x , then sec x + tan x =
(a) x , 1/x
(b) 2x , 1/2x
(c) −2x , 1/2x
(d) −1/x , x Watch Solution -
If π/2 < x < 3π/2 , then √((1 − sin x)/(1 + sin x)) is equal to
(a) sec x − tan x
(b) sec x + tan x
(c) tan x − sec x
(d) none of these Watch Solution -
If π < x < 2π , then √((1 + cos x)/(1 − cos x)) is equal to
(a) cosec x + cot x
(b) cosec x − cot x
(c) − cosec x + cot x
(d) − cosec x − cot x Watch Solution -
If 0 < x < π/2 , and if (y + 1)/(1 − y) = √((1 + sin x)/(1 − sin x)) , then y is equal to
(a) cot x/2
(b) tan x/2
(c) cot x/2 + tan x/2
(d) cot x/2 − tan x/2 Watch Solution -
If π/2 < x < π, then √((1 − sin x)/(1 + sin x)) + √((1 + sin x)/(1 − sin x)) is equal to
(a) 2 sec x
(b) −2 sec x
(c) sec x
(d) − sec x Watch Solution -
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x² + y² + z² is independent of
(a) θ, ϕ
(b) r, θ
(c) r, ϕ
(d) r Watch Solution -
If tan x + sec x = √3, 0 < x < π, then x is equal to
(a) 5π/6
(b) 2π/3
(c) π/6
(d) π/3 Watch Solution -
If tan x = −1/√5 and x lies in the IV quadrant, then the value of cos x is
(a) √5/√6
(b) 2/√6
(c) 1/2
(d) 1/√6 Watch Solution -
If 3π/4 < α < π, then √(2 cot α + 1/sin² α) is equal to
(a) 1 − cot α
(b) 1 + cot α
(c) −1 + cot α
(d) −1 − cot α Watch Solution -
sin⁶ A + cos⁶ A + 3 sin² A cos² A =
(a) 0
(b) 1
(c) 2
(d) 3 Watch Solution -
If cosec x − cot x = 1/2 , 0 < x < π/2 , then cos x is equal to
(a) 5/3
(b) 3/5
(c) −3/5
(d) −5/3 Watch Solution -
If cosec x + cot x = 11/2 , then tan x =
(a) 21/22
(b) 15/16
(c) 44/117
(d) 117/44 Watch Solution -
sec² x = 4xy/(x + y)² is true if and only if
(a) x + y ≠ 0
(b) x = y, x ≠ 0
(c) x = y
(d) x ≠ 0, y ≠ 0 Watch Solution -
If x is an acute angle and tan x = 1/√7 , then the value of (cosec² x − sec² x)/(cosec² x + sec² x) is
(a) 3/4
(b) 1/2
(c) 2
(d) 5/4 Watch Solution -
The value of sin² 5° + sin² 10° + sin² 15° + … + sin² 85° + sin² 90° is
(a) 7
(b) 8
(c) 9.5
(d) 10 Watch Solution -
sin² π/18 + sin² 2π/9 + sin² 7π/18 + sin² 4π/9 =
(a) 1
(b) 4
(c) 2
(d) 0 Watch Solution -
If tan A + cot A = 4, then tan⁴ A + cot⁴ A is equal to
(a) 110
(b) 191
(c) 80
(d) 194 Watch Solution -
If x sin 45° cos² 60° = (tan² 60° cosec 30°)/(sec 45° cot² 30°) , then x =
(a) 2
(b) 4
(c) 8
(d) 16 Watch Solution -
If A lies in second quadrant and 3 tan A + 4 = 0, then the value of 2 cot A − 5 cos A + sin A is equal to
(a) −53/10
(b) 23/10
(c) 37/10
(d) 7/10 Watch Solution -
If cosec x + cot x = 11/2 , then tan x =
(a) 21/22
(b) 15/16
(c) 44/117
(d) 117/43 Watch Solution -
If tan θ + sec θ = eˣ, then cos θ equals
(a) (eˣ + e⁻ˣ)/2
(b) 2/(eˣ + e⁻ˣ)
(c) (eˣ − e⁻ˣ)/2
(d) (eˣ − e⁻ˣ)/(eˣ + e⁻ˣ) Watch Solution -
If sec x + tan x = k, cos x =
(a) (k² + 1)/2k
(b) 2k/(k² + 1)
(c) k/(k² + 1)
(d) k/(k² − 1) Watch Solution -
If f(x) = cos² x + sec² x, then
(a) f(x) < 1
(b) f(x) = 1
(c) 1 < f(x) < 2
(d) f(x) ≥ 2 Watch Solution -
Which of the following is incorrect?
(a) sin x = −1/5
(b) cos x = 1
(c) sec x = 1/2
(d) tan x = 20 Watch Solution -
The value of cos 1° cos 2° cos 3° … cos 179° is
(a) 1/√2
(b) 0
(c) 1
(d) −1 Watch Solution -
The value of tan 1° tan 2° tan 3° … tan 89° is
(a) 0
(b) 1
(c) 1/2
(d) not defined Watch Solution -
Which of the following is correct?
(a) sin 1° > sin 1
(b) sin 1° < sin 1
(c) sin 1° = sin 1
(d) sin 1° = π/180 sin 1 Watch Solution -
If tan θ = −4/3, then sin θ is equal to
(a) −4/5 but not 4/5
(b) −4/5 or 4/5
(c) 4/5 but not −4/5
(d) none of these Watch Solution -
If sin θ and cos θ are the roots of the equation ax² − bx + c = 0, then a, b and c satisfy the relation
(a) a² + b² + 2ac = 0
(b) a² − b² + 2ac = 0
(c) a² + c² + 2ab = 0
(d) a² − b² − 2ac = 0 Watch Solution -
If sin θ + cosec θ = 2, then sin² θ + cosec² θ is equal to
(a) 1
(b) 4
(c) 2
(d) none of these Watch Solution -
Which of the following is incorrect?
(a) sin θ = −1/5
(b) cos θ = 1
(c) sec θ = 1/2
(d) tan θ = 20 Watch Solution -
If for real values of x, cos θ = x + 1/x , then
(a) θ is an acute angle
(b) θ is a right angle
(c) θ is an obtuse angle
(d) No value of θ is possible Watch Solution