Aptitude · all questions

Trigonometry
practice.

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357

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Q261

Open question

x = \frac{2 sin θ}{1 + cos θ + sin θ},

then the value of

\frac{1 - cos θ + sin θ}{1 + sin θ}

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Q262

Open question

If tan4θ = cot(40° - 2θ), then θ is equal to:

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Q263

Open question

What is the value of

\frac{32 cos ^{6} x - 48 cos ^{4} x + 18 cos ^{2} x - 1}{4 sin x cos x sin ( 60 - x ) cos ( 60 - x ) sin ( 60 + x ) cos ( 60 + x )} ?

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Q264

Open question

(\frac{tan ^{3} θ}{sec ^{2} θ} + \frac{cot ^{3} θ}{cose c ^{2} θ} + 2 sin θ cos θ)

÷ (1 + cosec²θ + tan²θ), 0° < θ < 90°, is equal to:

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Q265

Open question

The expression

\frac{( 1 - sin θ + cos θ ) ^{2} ( 1 - cos θ ) sec ^{3} θ cose c ^{2} θ}{( sec θ - tan θ ) ( tan θ + cot θ )},

0° < θ < 90°, is equal to:

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Q266

Open question

\frac{tan θ + sin θ}{tan θ - sin θ} = \frac{k + 1}{k - 1},

then k = ?

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Q267

Open question

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

then cosθ is equal to:

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Q268

Open question

(\frac{tan θ - sec θ + 1}{tan θ + sec θ - 1}) sec θ = \frac{1}{k},

then k = . . . . . . . .

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Q269

Open question

The value of m[sinθ + 2cos²∅ + 3sinθ + 4cos²∅ + . . . . . . . . + 18cos²∅] is a perfect square of an integer, θ = 30°, ∅ = 45° and 150 ≤ m ≤ 180. Find the value of m.

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Q270

Open question

If 1 + sin²θ - 3sinθcosθ = 0, then the value of cotθ is:

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Q271

Open question

The value of

\frac{3 ( cot ^{2} 47 ^{\circ} - sec ^{2} 43 ^{\circ} ) - 2 ( tan ^{2} 23 ^{\circ} - cose c ^{2} 67 ^{\circ} )}{cose c ^{2} ( 68 ^{\circ} + θ ) - tan ( θ + 61 ^{\circ} ) - tan ^{2} ( 22 ^{\circ} - θ ) + cot ( 29 ^{\circ} - θ )} is:

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Q272

Open question

\frac{( 2 sin A ) ( 1 + sin A )}{1 + sin A + cos A}

is equal to:

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Q273

Open question

\frac{sec θ - tan θ}{sec θ + tan θ} = \frac{1}{7}, θ,

lies in first quadrant, then the value of

\frac{cosec θ + cot ^{2} θ}{cosec θ - cot ^{2} θ}

is:

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Q274

Open question

The value of

\frac{sin ( 78 ^{\circ} + θ ) - cos ( 12 ^{\circ} - θ ) + ( tan ^{2} 70 ^{\circ} - cose c ^{2} 20 ^{\circ} )}{sin 25 ^{\circ} cos 65 ^{\circ} + cos 25 ^{\circ} sin 65 ^{\circ}} is:

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Q275

Open question

The value of

\frac{2 tan 60 ^{\circ}}{1 + tan ^{2} 60 ^{\circ}} = ?

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Q276

Open question

The expression (tanθ + cotθ)(secθ + tanθ)(1 - sinθ), 0° < θ < 90° is equal to:

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Q277

Open question

The value of

\frac{4 tan ^{2} 30 ^{\circ} + sin ^{2} 30 ^{\circ} cos ^{2} 45 ^{\circ} + sec ^{2} 48 ^{\circ} - cot ^{2} 42 ^{\circ}}{cos 37 ^{\circ} sin 53 ^{\circ} + sin 37 ^{\circ} cos 53 ^{\circ} + tan 18 ^{\circ} tan 72 ^{\circ}} is:

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Q278

Open question

If 4sin²θ = 3(1 + cosθ), 0° < θ < 90°, then what is the value of (2tanθ + 4sinθ - secθ)?

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Q279

Open question

The expression (cos⁶θ + sin⁶θ - 1)(tan²θ + cot²θ + 2) + 3 is equal to:

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Q280

Open question

If 5sinθ - 4cosθ = 0, 0° < θ < 90°, then the value of

\frac{5 sin θ - 2 cos θ}{5 sin θ + 3 cos θ}

is:

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Trigonometrypractice.

Trigonometry
practice.