Value of Trigonometric Functions at Multiples and Submultiples of an angle – Multiple Choice Questions (MCQs) Exercise Solutions
Mark the correct alternative in each of the following:
- 8 sin(x/8) cos(x/2) cos(x/4) cos(x/8) is equal to
(a) 8 cos x
(b) cos x
(c) 8 sin x
(d) sin x Watch Solution - (sec 8A − 1)/(sec 4A − 1) is equal to
(a) tan 2A / tan 8A
(b) tan 8A / tan 2A
(c) cot 8A / cot 2A
(d) none of these Watch Solution - The value of cos(π/65) cos(2π/65) cos(4π/65) cos(8π/65) cos(16π/65) cos(32π/65) is
(a) 1/8
(b) 1/16
(c) 1/32
(d) none of these Watch Solution - If cos 2x + 2 cos x = 1 then, (2 − cos²x) sin²x is equal to
(a) 1
(b) −1
(c) −√5
(d) √5 Watch Solution - For all real values of x, cot x − 2 cot 2x is equal to
(a) tan 2x
(b) tan x
(c) −cot 3x
(d) none of these Watch Solution - The value of 2 tan(π/10) + 3 sec(π/10) − 4 cos(π/10) is
(a) 0
(b) √5
(c) 1
(d) none of these Watch Solution - If in a ΔABC, tan A + tan B + tan C = 0, then cot A cot B cot C =
(a) 6
(b) 1
(c) 1/6
(d) none of these Watch Solution - If cos x = 1/2 (a + 1/a), and cos 3x = λ(a³ + 1/a³), then λ =
(a) 1/4
(b) 1/2
(c) 1
(d) none of these Watch Solution - If 2 tan α = 3 tan β, then tan(α − β) =
(a) sin 2β/(5 − cos 2β)
(b) cos 2β/(5 − cos 2β)
(c) sin 2β/(5 + cos 2β)
(d) none of these Watch Solution - If tan α = (1 − cos β)/sin β, then
(a) tan 3α = tan 2β
(b) tan 2α = tan β
(c) tan 2β = tan α
(d) none of these Watch Solution - If sin α + sin β = a and cos α − cos β = b, then tan((α − β)/2) =
(a) −a/b
(b) −b/a
(c) √(a² + b²)
(d) none of these Watch Solution - The value of (cot(x/2) − tan(x/2))² (1 − 2 tan x cot 2x) is
(a) 1
(b) 2
(c) 3
(d) 4 Watch Solution - The value of tan x sin(π/2 + x) cos(π/2 − x) is
(a) 1
(b) −1
(c) (1/2) sin 2x
(d) none of these Watch Solution - The value of sin²(π/18) + sin²(π/9) + sin²(7π/18) + sin²(4π/9) is
(a) 1
(b) 2
(c) 4
(d) none of these Watch Solution - If 5 sin α = 3 sin(α + 2β) ≠ 0, then tan(α + β) is equal to
(a) 2 tan β
(b) 3 tan β
(c) 4 tan β
(d) 6 tan β Watch Solution - The value of 2 cos x − cos 3x − cos 5x − 16 cos³x sin²x is
(a) 2
(b) 1
(c) 0
(d) −1 Watch Solution - If A = 2 sin²x − cos 2x, then A lies in the interval
(a) [−1, 3]
(b) [1, 2]
(c) [−2, 4]
(d) none of these Watch Solution - The value of cos 3x/(2 cos 2x − 1) is equal to
(a) cos x
(b) sin x
(c) tan x
(d) none of these Watch Solution - If tan(π/4 + x) + tan(π/4 − x) = λ sec 2x, then
(a) 3
(b) 4
(c) 1
(d) 2 Watch Solution - The value of cos²(π/6 + x) − sin²(π/6 − x) is
(a) (1/2) cos 2x
(b) 0
(c) −(1/2) cos 2x
(d) 1/2 Watch Solution - The value of sin 3x/(1 + 2 cos 2x) is equal to
(a) cos x
(b) sin x
(c) −cos x
(d) sin x Watch Solution - The value of 2 sin²B + 4 cos(A + B) sin A sin B + cos 2(A + B) is
(a) 0
(b) cos 3A
(c) cos 2A
(d) none of these Watch Solution - The value of 2(sin 2x + 2 cos²x − 1)/(cos x − sin x − cos 3x + sin 3x) is
(a) cos x
(b) sec x
(c) cosec x
(d) sin x Watch Solution - 2(1 − 2 sin²7x) sin 3x is equal to
(a) sin 17x − sin 11x
(b) sin 11x − sin 17x
(c) cos 17x − cos 11x
(d) cos 17x + cos 11x Watch Solution - If α and β are acute angles satisfying cos 2α = (3 cos 2β − 1)/(3 − cos 2β), then tan α =
(a) √2 tan β
(b) (1/√2) tan β
(c) √2 cot β
(d) (1/√2) cot β Watch Solution - If tan(x/2) = √((1 − e)/(1 + e)) tan(α/2), then cos α =
(a) (1 + e cos x)/(cos x + e)
(b) (1 + e cos x)/(cos x − e)
(c) (1 − e cos x)/(cos x − e)
(d) (cos x − e)/(1 − e cos x) Watch Solution - If (2ⁿ + 1)x = π, then 2ⁿ cos x cos 2x cos 2²x … cos 2ⁿ⁻¹x =
(a) −1
(b) 1
(c) 1/2
(d) none of these Watch Solution - If tan x = t then tan 2x + sec 2x is equal to
(a) (1 + t)/(1 − t)
(b) (1 − t)/(1 + t)
(c) 2t/(1 − t)
(d) 2t/(1 + t) Watch Solution - The value of cos⁴x + sin⁴x − 6 cos²x sin²x is
(a) cos 2x
(b) sin 2x
(c) cos 4x
(d) none of these Watch Solution - The value of cos(36° − A) cos(36° + A) + cos(54° − A) cos(54° + A) is
(a) cos 2A
(b) sin 2A
(c) cos A
(d) 0 Watch Solution - The value of tan x tan(π/3 − x) tan(π/3 + x) is
(a) cot 3x
(b) 2 cot 3x
(c) tan 3x
(d) 3 tan 3x Watch Solution - The value of tan x + tan(π/3 + x) + tan(2π/3 + x) is
(a) 3 tan 3x
(b) tan 3x
(c) 3 cot 3x
(d) cot 3x Watch Solution - The value of (sin 5α − sin 3α)/(cos 5α + 2 cos 4α + cos 3α) is
(a) cot(α/2)
(b) cot α
(c) tan(α/2)
(d) none of these Watch Solution - The value of sin 5x/sin x is equal to
(a) 16 cos⁴x − 12 cos²x + 1
(b) 16 cos⁴x + 12 cos²x + 1
(c) 16 cos⁴x − 12 cos²x − 1
(d) 16 cos⁴x + 12 cos²x − 1 Watch Solution - If n = 1, 2, 3, …, then cos α cos 2α cos 4α … cos 2ⁿ⁻¹α is equal to
(a) sin 2nα/(2n sin α)
(b) sin 2ⁿα/(2ⁿ sin 2ⁿ⁻¹α)
(c) sin 4ⁿ⁻¹α/(4ⁿ⁻¹ sin α)
(d) sin 2ⁿα/(2ⁿ sin α) Watch Solution - If tan x = a/b, then b cos 2x + a sin 2x is equal to
(a) a
(b) b
(c) a/b
(d) b/a Watch Solution - If tan α = 1/7, tan β = 1/3, then cos 2α is equal to
(a) sin 2β
(b) sin 4β
(c) sin 3β
(d) cos 2β Watch Solution - The value of cos²48° − sin²12° is
(a) (√5 + 1)/8
(b) (√5 − 1)/8
(c) (√5 + 1)/5
(d) (√5 + 1)/(2√2) Watch Solution - The value of (1 − tan²15°)/(1 + tan²15°) is
(a) 1
(b) √3
(c) √3/2
(d) 2 Watch Solution - The value of tan75° − cot75° is
(a) 2√3
(b) 2 + √3
(c) 2 − √3
(d) 1 Watch Solution - cos2θ cos2ϕ + sin²(θ − ϕ) − sin²(θ + ϕ) is equal to
(a) sin2(θ + ϕ)
(b) cos2(θ + ϕ)
(c) sin2(θ − ϕ)
(d) cos2(θ − ϕ) Watch Solution - If tan A = 1/2, tan B = 1/3, then tan(2A + B) is equal
(a) 1
(b) 2
(c) 3
(d) 4 Watch Solution - If sin θ + cos θ = 1, then the value of sin2θ is equal to
(a) 1
(b) 1/2
(c) 0
(d) −1 Watch Solution - The value of sin(π/10) sin(13π/10) is
(a) 1/2
(b) −1/2
(c) −1/4
(d) 1 Watch Solution - If sin θ = −4/5 and θ lies in third quadrant, then the value of cos(θ/2) is
(a) 1/5
(b) −1/√10
(c) −1/√5
(d) 1/√10 Watch Solution - The value of cos12° + cos84° + cos156° + cos132° is
(a) 1/2
(b) 1
(c) −1/2
(d) −1/8 Watch Solution
Chapter 9: Values of Trigonometric Functions at Multiples and Submultiples of an Angle – R. D. Sharma Class 11th Maths
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Values of Trigonometric Functions at Multiples and Submultiples of an Angle Exercise 9.1 Video Solution
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Values of Trigonometric Functions at Multiples and Submultiples of an Angle Exercise 9.2 Video Solution
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Values of Trigonometric Functions at Multiples and Submultiples of an Angle Exercise 9.3 Video Solution
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Values of Trigonometric Functions at Multiples and Submultiples of an Angle Multiple Choice Questions (MCQs) Video Solution Video Solution
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Values of Trigonometric Functions at Multiples and Submultiples of an Angle Fill in the Blanks (FBQs) Video Solution
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Values of Trigonometric Functions at Multiples and Submultiples of an Angle Very Short Answer Questions (VSAQs) Video Solution Video Solution