Daily Math · 2026-05-27

Question 1

Find $\sin 75° - \sin 15°$.

Accepted Answer

$\bullet$ Apply the difference-to-product identity:

$$\sin A - \sin B = 2\cos	frac{A+B}{2}\sin	frac{A-B}{2}$$

$\bullet$ With $A=75°$, $B=15°$ the half-sum is $45°$ and half-difference is $30°$:

$$\sin 75° - \sin 15° = 2\cos 45°\sin 30°$$

$\bullet$ Evaluate:

$$2\cdot	frac{\sqrt{2}}{2}\cdot	frac{1}{2} = 	frac{\sqrt{2}}{2}$$

Answer

$\dfrac{\sqrt{6}}{2}$

Answer

$\dfrac{\sqrt{2}}{2}$

Answer

$\dfrac{\sqrt{3}}{2}$

Answer

$\dfrac{1}{2}$

Answer

$1$

Answer

$\dfrac{\sqrt{2}}{4}$

Question 2

The remainder of the division of $P(X) = X^3 + 2X^2 - X + 5$ by $X - 1$ is:

Accepted Answer

$P(1) = 1 + 2 - 1 + 5 = 7$.

Answer

$0$

Answer

$5$

Answer

$7$

Answer

$9$

Question 3

For $f$ continuous and non-negative on $[a, b]$ with $b > a$:

Accepted Answer

The integral of a non-negative continuous function over $[a, b]$ is non-negative (representing the area under the curve).

Answer

$\int_a^b f < 0$ always

Answer

$\int_a^b f = 0$ always

Answer

$\int_a^b f \ge 0$

Answer

$\int_a^b f$ depends only on $b$

Problems & worked solutions