81.

If cot(α) and cot(β) are the roots of the equation x² – 3x + 2 = 0, then what is cot (α + β) equal to ?

• $\frac{1}{2}$

• $\frac{1}{3}$

• 2

• 3

If sin(x) + sin(y) = cos(y) – cos(x), where $0 < \mathrm{y} < \mathrm{x} < \frac{\mathrm{\pi }}{2}$

then what is $\tan \left(\frac{\mathrm{x} - \mathrm{y}}{2}\right)$ equal to ?

• 0

• $\frac{1}{2}$

• 1

• 2

$\mathrm{Let} \mathrm{\alpha } = \mathrm{\beta } = 15°$

What is sin(α + 1^o) + cos(β + 1^o) equal to ?

• $\sqrt{3}\cos \left(1°\right) + \sin \left(1°\right)$

• $\sqrt{3}\cos \left(1°\right) - \frac{1}{2}\sin \left(1°\right)$

• $\frac{1}{\sqrt{2}}\left(\sqrt{3}\cos \left(1°\right) - \sin \left(1°\right)\right)$

• $\frac{1}{\sqrt{2}}\left(\cos \left(1°\right) - \sin \left(1°\right)\right)$

$\mathrm{Let} \mathrm{\alpha } = \mathrm{\beta } = 15°$

What is the value of sin(7α) -cos(7β) ?

• $\frac{1}{\sqrt{2}}$

• $\frac{1}{2\sqrt{2}}$

• $\frac{\sqrt{3}}{2\sqrt{2}}$

• $\frac{\sqrt{3}}{\sqrt{2}}$

$\mathrm{Let} \mathrm{\alpha } = \mathrm{\beta } = 15°$

What is the value of sin(α) + cos(β) ?

• $\frac{1}{\sqrt{2}}$

• $\frac{1}{2\sqrt{2}}$

• $\frac{\sqrt{3}}{2\sqrt{2}}$

• $\frac{\sqrt{3}}{\sqrt{2}}$

Let t_n = sinⁿ(θ) + cosⁿ(θ)

What is the value of t₁₀ where θ = 45^o ?

• 1

• $\frac{1}{4}$

• $\frac{1}{16}$

• $\frac{1}{32}$

Let t_n = sinⁿ(θ) + cosⁿ(θ)

What is the value of t₁²  - t₂ = ?

• $\cos \left(2\mathrm{\theta }\right)$

• $\sin \left(2\mathrm{\theta }\right)$

• $2\cos \left(\mathrm{\theta }\right)$

• $2\sin \left(\mathrm{\theta }\right)$

Let t_n = sinⁿ(θ) + cosⁿ(θ)

What is $\frac{{\mathrm{t}}_3 - {\mathrm{t}}_5}{{\mathrm{t}}_5 - {\mathrm{t}}_7}$ = ?

• $\frac{{\mathrm{t}}_1}{{\mathrm{t}}_3}$

• $\frac{{\mathrm{t}}_3}{{\mathrm{t}}_5}$

• $\frac{{\mathrm{t}}_5}{{\mathrm{t}}_7}$

• $\frac{{\mathrm{t}}_1}{{\mathrm{t}}_7}$

Let asin²(x) + bcos²(x) = c; bsin²(y) + acos²(y) = d and p tan(x) = qtan(y).

What is $\frac{{\mathrm{p}}^2}{{\mathrm{q}}^2}$ equal to?

• $\frac{\left(\mathrm{b} - \mathrm{c}\right)\left(\mathrm{b} - \mathrm{d}\right)}{\left(\mathrm{a} - \mathrm{d}\right)\left(\mathrm{a} - \mathrm{c}\right)}$

• $\frac{\left(\mathrm{a} - \mathrm{d}\right)\left(\mathrm{c} - \mathrm{a}\right)}{\left(\mathrm{b} - \mathrm{c}\right)\left(\mathrm{d} - \mathrm{b}\right)}$

• $\frac{\left(\mathrm{d} - \mathrm{a}\right)\left(\mathrm{c} - \mathrm{a}\right)}{\left(\mathrm{b} - \mathrm{c}\right)\left(\mathrm{d} - \mathrm{b}\right)}$

• $\frac{\left(\mathrm{b} - \mathrm{c}\right)\left(\mathrm{b} - \mathrm{d}\right)}{\left(\mathrm{c} - \mathrm{a}\right)\left(\mathrm{a} - \mathrm{d}\right)}$

Let asin²(x) + bcos²(x) = c; bsin²(y) + acos²(y) = d and p tan(x) = qtan(y).

What is $\frac{\mathrm{d} - \mathrm{a}}{\mathrm{b} - \mathrm{d}}$ equal to ?

• sin²(y)

• cos²(y)

• tan²(y)

• cot²(y)