Aptitude · all questions

Trigonometry
practice.

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357

Questions

12/18

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Q221

Open question

sec θ + \frac{1}{cos θ} = 2,

find the value of

sec^{55} θ + \frac{1}{sec ^{55} θ} = ?

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Q222

Open question

Simplify the following expression:

\frac{cos A}{1 - tan A} + \frac{sin A}{1 - cot A} - sin A

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Q223

Open question

If sinA =

\frac{5}{13}

and 7cotB = 24, then the value of (secAcosB)(cosecBtanA) is:

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Q224

Open question

\frac{1 + cos θ - sin ^{2} θ}{sin θ ( 1 + cos θ )} \times \frac{sec ^{2} θ + cose c ^{2} θ}{tan θ + cot θ},

0° < θ < 90°, is equal to:

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Q225

Open question

The value of

\frac{sin 23 ^{\circ} cos 67 ^{\circ} + sec 52 ^{\circ} sin 38 ^{\circ} + cos 23 ^{\circ} sin 67 ^{\circ} + cosec 52 ^{\circ} cos 38 ^{\circ}}{cose c ^{2} 20 ^{\circ} - tan ^{2} 70 ^{\circ}} is:

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Q226

Open question

{(\frac{sec θ - 1}{sec θ + 1})}^{n} = cosec θ - cot θ,

then n = ?

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Q227

Open question

If cosθ =

\frac{12}{13},

then the value of

\frac{sin θ ( 1 - tan θ )}{tan θ ( 1 + cosec θ )}

is:

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Q228

Open question

If 2cos²θ + 3sinθ = 3, where 0° < θ < 90°, then what is the value of sin²2θ + cos²θ + tan²2θ + cosec²2θ?

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Q229

Open question

\frac{sin ^{2} θ}{cos ^{2} θ - 3 cos θ + 2} = 1, θ

lies in the first quadrant, then the value of

\frac{tan ^{2} \frac{θ}{2} + sin ^{2} \frac{θ}{2}}{tan θ + sin θ}

is:

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Q230

Open question

The value of the expression (cos⁶θ + sin⁶θ - 1)(tan²θ + cot²θ + 2) is:

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Q231

Open question

If sec²A + tan²A = 3, then what is the value of cotA?

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Q232

Open question

The value of 4sin²30° + 3cot²60° is:

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Q233

Open question

The value of

1 + \frac{cot θ + cos θ}{cot θ - cos θ},

if 0° < θ < 90°, is equal to:

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Q234

Open question

What is the value of 5sin²60° + 7sin²45°+ 8cos²45°?

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Q235

Open question

What is the value of

\frac{cos 40 ^{\circ} - cos 140 ^{\circ}}{sin 80 ^{\circ} + sin 20 ^{\circ}} ?

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Q236

Open question

(sinθ + cosecθ)² + (cosθ + secθ)² - 1 = . . . . . . . .

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Q237

Open question

If sec4θ = cosec(θ + 20°), then θ is equal to:

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Q238

Open question

What is the value of the expression cos2Acos2B + sin²(A - B) - sin²(A + B)?

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Q239

Open question

The value of

\frac{( cos 9 ^{\circ} + sin 81 ^{\circ} ) ( sec 9 ^{\circ} + cosec 81 ^{\circ} )}{sin 56 ^{\circ} sec 34 ^{\circ} + cos 25 ^{\circ} cosec 65 ^{\circ}} is:

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Q240

Open question

If 7sin²θ + 4cos²θ = 5 and θ lies in the first quadrant, then what is the value of

\frac{3 sec θ + tan θ}{2 cot θ - 3 cos θ} ?

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Trigonometrypractice.

Trigonometry
practice.