Write the value of 12 5 12 . - Vidyadip

Question

Write the value of $\sin\frac{\pi}{12}\sin\frac{5\pi}{12}.$

✓

Answer

We have,
$\sin\frac{\pi}{12}\sin\frac{5\pi}{12}=\frac{1}{2}\Big[2\sin\frac{\pi}{12}+\sin\frac{5\pi}{12}\Big]$
$=\ \frac{1}{2}\Big[\cos\Big(\frac{\pi}{12}-\frac{5\pi}{12}\Big)-\cos\Big(\frac{\pi}{12}+\frac{5\pi}{12}\Big)\Big]$
$=\ \frac{1}{2}\Big[\cos\Big(\frac{-4\pi}{12}\Big)-\cos\Big(\frac{6\pi}{12}\Big)\Big]$
$=\ \frac{1}{2}\Big[\cos\frac{\pi}{3}-\cos\frac{\pi}{2}\Big]$
$=\ \frac{1}{2}\Big[\frac{1}{2}-0\Big]$
$=\ \frac{1}{4}$
$\therefore\ \text{Value of }\sin\frac{\pi}{12}\sin\frac{5\pi}{12}=\frac{1}{4}.$

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 "1 Marks Question" from Transformation Formulae→Transformation Formulae — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Which of the following can not be valid assignment of probabilities for outcomes of sample Space S = $\{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}, \omega_{5}, \omega_{6}, \omega_{7}\}$

Assignment	$\omega_{1}$	$\omega_{2}$	$\omega_{3}$	$\omega_{4}$	$\omega_{5}$	$\omega_{6}$	$\omega_{7}$
	-0.1	0.2	0.3	0.4	-0.2	0.1	0.3

Write the standard value of the limit $\lim _{x \rightarrow \infty}\left(1+\frac{1}{x}\right)^x.$

Let A = {1, 2, {3, 4 }, 5}. Is the statement {{3, 4}} $\subset$ A is incorrect and why?

State the converse and contrapositive of the following statements:
A positive integer is prime only if it has no divisors other than 1 and itself.

Describe the following sets in Roster form:
{x ∈ N : x is a prime number, 10 < x < 20};

Write down the negation of following compound statement:
All rational numbers are real and complex.

P(A)	P(B)	P(A$\cap$B)	P(A$\cup$B)
$\frac 13$	$\frac 15$	$\frac 1{15}$	_____

Convert 40° 20′ into radian measure.

Write the value of $\frac{\text{d}}{\text{dx}}(\text{x}|\text{x}|)$

Write the negation of the following statements:
It rained on July 4, 2005.