Prove that: 2 5 12 12 =1 2 - Vidyadip

Question

Prove that:
$2\cos\frac{5\pi}{12}\cos\frac{\pi}{12}=\frac{1}{2}$

✓

Answer

$\text{LHS}=2\cos\frac{5\pi}{12}\cos\frac{\pi}{12}$
$\because\ 2\cos\text{A}\cos\text{B}=\cos(\text{A+B})+\cos(\text{A}-\text{B})$
$=\ \cos\Big(\frac{5\pi}{12}+\frac{\pi}{12}\Big)+\cos\Big(\frac{5\pi}{12}-\frac{\pi}{12}\Big)$
$=\ \cos\Big(\frac{\pi}{2}\Big)+\cos\Big(\frac{\pi}{3}\Big)$
$=\ 0+\frac{1}{2}=\frac{1}{2}=\text{RHS}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the following Question.(1 Marks)" from Transformation Formulae→Transformation Formulae — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Compute:
$\left(\frac{12}{6}\right) !$

Write the value of $\sum\limits_\text{r-1}^6 {^\text{56-r}}\text{C}_{\text{3}}+{^\text{50}}\text{C}_{\text{4}}.$

Evaluate the following : $\sin \pi+2 \cos \pi+3 \sin \frac{3 \pi}{2}+4 \cos \frac{3 \pi}{2} \ -5 \sec \pi-6 \operatorname{cosec} \frac{3 \pi}{2}$

Find out the following sentences are statements and which are not. Justify your answer.
All triangles have three sides.

State the converse and contrapositive of the following statements:
I go to a beach whenever it is a sunny day.

Differentiate the following w.r.t. x :

$y =x^{\frac{4}{3}}+e^x-\sin x$

Given an example of a statement P(n) such that it is true for all $\text{n}\in\text{N}.$

A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space for this experiment.

Evaluate the following limits:
$\lim\limits_{\text{x}\rightarrow1}\frac{\text{x}^2+1}{\text{x}+1}$

Write the solution set of x satisfying the inequation $|\text{x}-1|\leq3$ and $|\text{x}-1|\leq1.$