Aptitude · all questions

Trigonometry
practice.

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Q301

Let

a = \frac{2 sin x}{1 + sin x + cos x}

and

b = \frac{c}{1 + sin x} .

Then a = b, if c = ?

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Q302

The value of

\frac{sec θ ( 1 - sin θ ) ( sin θ + cos θ ) ( sec θ + tan θ )}{sin θ ( 1 + tan θ ) + cos θ ( 1 + cot θ )}

is equal to:

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Q303

If A + B = C, then tanAtanBtanC = ?

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Q304

The value of expression cos²45° + cos²135° + cos²225° + cos²315° is:

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Q305

What is the value of 3sin²30° +

\frac{3}{5}

cos²60° - 2sec²45°?

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Q306

What is the value of

1 + \frac{tan ^{2} A}{1 + sec A} ?

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Q307

Solve the following to find its value in terms of trigonometric ratios.
(sinA + cosA)(1 - sinAcosA)

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Q308

What is the value of

sin (180 - θ) sin (90 - θ) + \frac{cot ( 90 - θ )}{1 + tan ^{2} θ} ?

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Q309

What is the value of

\frac{( sin 4 x + sin 4 y ) [ tan ( 2 x - 2 y ) ]}{sin 4 x - sin 4 y} ?

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Q310

If cos⁴α - sin⁴α =

\frac{5}{6}

then the value of 2cos²α - 1 = . . . . . . . .

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Q311

If P + Q + R = 60°, then what is the value of cosQcosR(cosP - sinP) + sinQsinR(sinP - cosP)?

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Q312

The value of

[\frac{sin ^{2} 24 ^{\circ} + sin ^{2} 66 ^{\circ}}{cos ^{2} 24 ^{\circ} + cos ^{2} 66 ^{\circ}} + sin^{2} 61^{\circ} + cos 61^{\circ} sin 29^{\circ}]

is equal to

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Q313

What is

sin α - sin β = ?

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Q314

If 6tanA(tanA + 1) = 5 - tanA, given that 0 < A <

\frac{π}{2}

what is the value of (sinA + cosA)?

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Q315

If tan²A - 6tanA + 9 = 0, 0° < A < 90°, What is the value of 6cotA +

810

cosA?

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Q316

If √3tanθ = 3sinθ, then what is the value of sin²θ - cos²θ?

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Q317

If tanθ + cotθ = -2, then the value of tan⁹θ + cot⁹θ is:

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Q318

\frac{2 + tan ^{2} θ + cot ^{2} θ}{sec θ cosec θ}

is equal to:

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Q319

What is the value of

\frac{3 sin 58 ^{\circ}}{cos 32 ^{\circ}} + \frac{3 sin 42 ^{\circ}}{cos 48 ^{\circ}}

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Q320

sin⁴θ + cos⁴θ in terms of sinθ can be written as:

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