Prove that: 23^ + 37^ = 7^ - Vidyadip

Question

Prove that:
$\sin23^\circ+\sin37^\circ=\cos7^\circ$

✓

Answer

$\sin23^\circ+\sin37^\circ=\cos7^\circ$
$\text{LHS}=\sin23^\circ+\sin37^\circ$
$=\ 2\sin\Big(\frac{23^\circ+37^\circ}{2}\Big)\cos\Big(\frac{23^\circ-37^\circ}{2}\Big)$ $\Big[\because\ \sin\text{C}+\sin\text{D}=2\sin\frac{\text{C+D}}{2}\cos\frac{\text{C}-\text{D}}{2}\Big]$
$=\ 2\sin(30^\circ)\cos(-7^\circ)$
$=\ 2\times\frac{1}{2}\cos7^\circ\Big[\because\ \cos(-\theta)=\cos\theta,\sin30^\circ=\frac{1}{2}\Big]$
$=\ \cos7^\circ=\text{RHS}$

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.(2 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

Find $k$, if $A=\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right]$ and $A^2=K A-2$

Prove the following : $\frac{\cos x+\sin x}{\cos x-\sin x}-\frac{\cos x-\sin x}{\cos x+\sin x}=2 \tan 2 \mathrm{x}$

Find the general solutions of the following equations:$\text{cosec }\text{x}=-\sqrt{2}$

Prove that:
$\sin\Big(\frac{4\pi}{9}+\text{7}\Big)\cos\Big(\frac{\pi}{9}+\text{7}\Big)-\cos\Big(\frac{4\pi}{9}+\text{7}\Big)\sin\Big(\frac{\pi}{9}+\text{7}\Big)=\frac{\sqrt{3}}{2}$$ $

Find the values of x, if

$\left|\begin{array}{ccc}1 & 2 x & 4 x \\ 1 & 4 & 16 \\ 1 & 1 & 1\end{array}\right|=0$

Solve the following quadratic equations:

$8 x^2+2 x+1=0$

If $f, g, h$ are three function defined from $R$ to $R$ as follows:
$h(x) = x^2 + 1$

Prove that:
$\frac{\sin\text{x}+\sin2\text{x}}{1+\cos\text{x}+\cos2\text{x}}=\tan\text{x}$

Write the parametric equations of the circles:
$x^2+y^2+2 x-4 y-4=0$

A party has 20 participants. Find the number of distinct ways for the host to sit with them around a circular table. How many of these ways have two specified persons on either side of the host?