Prove that cos left( frac{pi}{4} + x right) + | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

We use the trigonometric identity $\cos A + \cos B = 2 \cos \left( \frac{A+B}{2} \right) \cos \left( \frac{A-B}{2} \right)$.Let $A = \frac{\pi}{4} + x

Vedclass · Accepted Answer

Vedclass · Answer

We use the trigonometric identity $\cos A + \cos B = 2 \cos \left( \frac{A+B}{2} \right) \cos \left( \frac{A-B}{2} \right)$.
Let $A = \frac{\pi}{4} + x$ and $B = \frac{\pi}{4} - x$.
Then,$\frac{A+B}{2} = \frac{(\frac{\pi}{4} + x) + (\frac{\pi}{4} - x)}{2} = \frac{\frac{\pi}{2}}{2} = \frac{\pi}{4}$.
And,$\frac{A-B}{2} = \frac{(\frac{\pi}{4} + x) - (\frac{\pi}{4} - x)}{2} = \frac{2x}{2} = x$.
Substituting these into the identity:
$L.H.S. = 2 \cos \left( \frac{\pi}{4} \right) \cos x$.
Since $\cos \left( \frac{\pi}{4} \right) = \frac{1}{\sqrt{2}}$,we have:
$L.H.S. = 2 \times \frac{1}{\sqrt{2}} \cos x = \sqrt{2} \cos x = R.H.S$.

Prove that $\cos \left( \frac{\pi}{4} + x \right) + \cos \left( \frac{\pi}{4} - x \right) = \sqrt{2} \cos x$.

Similar Questions

Prove that $\frac{\cos 7x + \cos 5x}{\sin 7x - \sin 5x} = \cot x$.

$\cos ^2\left(\frac{\pi}{6}+\theta\right)-\sin ^2\left(\frac{\pi}{6}-\theta\right)$ is equal to

If $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$,then $\cos 2A = $

Prove that $\cos \left(\frac{\pi}{4}-x\right) \cos \left(\frac{\pi}{4}-y\right)-\sin \left(\frac{\pi}{4}-x\right) \sin \left(\frac{\pi}{4}-y\right)=\sin (x+y)$

Determine the value of $a$ in $\tan 70^{\circ} - \tan 20^{\circ} = a \cdot \tan 50^{\circ} ?$

Vedclass Test Series

Exam Paper Generator

Online Exam Module