Aptitude · all questions

Trigonometry
practice.

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357

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6/18

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Q101

Open question

The numerical value of 1 +

\frac{1}{co t ^{2} 63 ^{\circ}}

se c^{2} 2 7^{\circ}

\frac{1}{sin ^{2} 63 ^{\circ}}

cose c^{2} 2 7^{\circ}

is?

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Q102

Open question

The value of

\frac{1}{2} sin \frac{π}{6}

cos \frac{π}{4}

cot \frac{π}{3}

sec \frac{π}{6}

\frac{5 tan \frac{π}{4}}{12 sin \frac{π}{2}}

is equal to?

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Q103

Open question

x sin^{2} 6 0^{\circ}

\frac{3}{2} sec 6 0^{\circ}

ta n^{2} 3 0^{\circ}

\frac{4}{5} sin^{2} 4 5^{\circ}

ta n^{2} 6 0^{\circ}

= 0, then x is?

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Q104

Open question

If 0° < A < 90°, then the value of tan²A + cot²A - sec²A cosec²A is?

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Q105

Open question

If α and β are positive acute angles, sin(4α - β) = 1 and cos(2α + β) =

\frac{1}{2},

then the value of sin(α + 2β) is?

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Q106

Open question

If θ is a positive acute angle and 4cos²θ - 1 = 0, then the value of tan(θ - 15°) is equal to?

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Q107

Open question

The value of

\frac{sin 25 ^{\circ} . cos 65 ^{\circ} + cos 25 ^{\circ} . sin 65 ^{\circ}}{tan ^{2} 70 ^{\circ} - cose c ^{2} 20 ^{\circ}}

is?

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Q108

Open question

θ + ϕ = \frac{π}{2}

and

sin θ = \frac{1}{2},

then the value of

sin ϕ

is?

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Q109

Open question

Find the value of the following 3(sin⁴θ + cos⁴θ) + 2(sin⁶θ + cos⁶θ) + 12sin²θ.cos²θ = ?

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Q110

Open question

The numerical value of

\frac{co s ^{2} 45 ^{\circ}}{sin ^{2} 60 ^{\circ}}

\frac{co s ^{2} 60 ^{\circ}}{sin ^{2} 45 ^{\circ}}

\frac{ta n ^{2} 30 ^{\circ}}{co t ^{2} 45 ^{\circ}}

\frac{sin ^{2} 30 ^{\circ}}{co t ^{2} 30 ^{\circ}}

is?

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Q111

Open question

sec θ - tan θ = \frac{1}{3},

the value of

sec θ

tan θ

= ?

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Q112

Open question

The value of (cosec a - sin a)(sec a - cos a)(tan a + cot a) is?

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Q113

Open question

The value of θ(0 ≤ θ ≤ 90°) satisfying 2sin²θ = 3cosθ is?

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Q114

Open question

a, b, c are the lengths of three sides of a triangle ABC. If a, b, c are related by the relation a² + b² + c² = ab + bc + ca, then the value of (sin²A + sin²B + sin²C) is?

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Q115

Open question

tan α = 2,

then the value of

\frac{cose c ^{2} α - se c ^{2} α}{cose c ^{2} α + se c ^{2} α}

is?

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Q116

Open question

sin (θ + 30^{\circ}) = \frac{3}{12},

then find

co s^{2} θ ?

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Q117

Open question

0 ⩽ θ ⩽ 9 0^{\circ}

and

4 cos^{2} θ

43 cos θ

+ 3 = 0 then the value of

θ

is?

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Q118

Open question

The value of sec⁴A(1 - sin⁴A) - 2tan²A is?

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Q119

Open question

co s^{4} θ - sin^{4} θ = \frac{2}{3},

then the value of

2co s^{2} θ - 1

is?

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Q120

Open question

sin θ - cos θ = \frac{7}{13}

and

0^{\circ} < θ < 9 0^{\circ},

then the value of

sin θ

cos θ

is?

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Trigonometrypractice.

Trigonometry
practice.