Simplify the following:
\(
\frac{\cos x - \sqrt{3}\sin x}{2}
\)
\(
\cos\!\left(\tfrac{\pi}{3} - x\right)
\)
\(
\sin\!\left(\tfrac{\pi}{3} + x\right)
\)
\(
\cos\!\left(\tfrac{\pi}{3} + x\right)
\)
\(
\sin\!\left(\tfrac{\pi}{3} - x\right)
\)
Find the value of the following expression.
\(
12^{3} + (-8)^{3} + (-4)^{3}
\)
Suppose ΔABC be a right-angled triangle where ∠A = 90° and AD ⊥ BC. If area (ΔABC) = 80 cm² and BC = 16 cm, then the length of AD is:
The following pie chart represents the percentage-wise weight distribution of different fruits out of 2500 kg of fruits at one fruit shop.
What is the difference between the weights of banana and orange at the fruit shop?
Rearrange the parts of the sentence in correct order.
A 2007-2009 study
P. explored forward thinking techniques
Q. to synchronise time on board deep
R. space probes for accurate navigation, in
S. particular looking into low-cost options