Download App

Transformation Formulae — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTransformation Formulae2 Marks
Question
Prove that: $\cos\frac{\pi}{12}-\sin\frac{\pi}{12}=\frac{1}{\sqrt2}$
✓

Answer

$\text{LHS}=\cos\frac{\pi}{12}-\sin\frac{\pi}{12}$ Multiplying and dividing by $\sqrt2$ on LHS $=\ \sqrt2\Big(\frac{1}{\sqrt2}\cos\frac{\pi}{12}-\frac{1}{\sqrt2}\sin\frac{\pi}{12}\Big)$ $=\ \sqrt2\Big(\sin\frac{\pi}{4}\cos\frac{\pi}{12}-\cos\frac{\pi}{4}\sin\frac{\pi}{12}\Big)$ $\Big[\because\ \frac{1}{\sqrt2}=\cos\frac{\pi}{4}=\sin\frac{\pi}{4}\Big]$ $=\ \sqrt2\Big(\sin\Big(\frac{\pi}{4}-\frac{\pi}{12}\Big)\Big)$ $[\because\ \sin(\text{A}-\text{B})=\sin\text{A}\cos\text{B}-\cos\text{A}\sin\text{B}$ $=\ \sqrt2\Big(\sin\frac{\pi}{6}\Big)$ $=\ \sqrt2\times\frac{1}{2}$ $=\ \frac{1}{\sqrt2}$ $=\ \text{RHS}$

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 "(Each question 2 marks)" from Transformation Formulae→Transformation Formulae — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Solve $\sqrt 2 \;{x^2} + x + \sqrt 2 = 0$
→
If $P(n)$ is the statement " $n^3+n$ is divisible by 3 ", prove that $P(3)$ is true but $P(4)$ is not true.
→
Let N be the set of natural numbers and the relation R be defined on N such that R = {(x, y) : y = 2x, x, y $\in$ N}. What is the domain, codomain and range of R? Is this relation a function?
→
Prove that: $2{\sin ^2}\frac{\pi }{6} + \cos e{c^2}\frac{{7\pi }}{6}{\cos ^2}\frac{\pi }{3} = \frac{3}{2}$
→
How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?
→
How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?
→
Solve the following system of equations in R. 3x - 6 > 0, 2x - 5 > 0
→
Let $z_1 = 2 - i, z_2 = -2 + i$. Find $\operatorname{Re} \left( {\frac{{{z_1}{z_2}}}{{{{\overline z }_1}}}} \right)$
→
Find the sum of the following arithmetic progression:
$9,\ \frac{9}{2},\ \frac{15}{2},\ ...$ to 25 terms.
→
Evaluate the following one sided limits: $\lim\limits_{\text{x}\rightarrow0^-}(1+\text{cosec }\text{x})$
→