frac{sin(B + A) + cos(B - A)}{sin(B - A) + co | vedclass

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

Question

(B) Given expression: $E = \frac{\sin(B + A) + \cos(B - A)}{\sin(B - A) + \cos(B + A)}$Using the identities $\cos 	heta = \sin(90^\circ - 	heta)$:$E

Vedclass · Accepted Answer

$\frac{\cos A + \sin A}{\cos A - \sin A}$

Vedclass · Answer

(B) Given expression: $E = \frac{\sin(B + A) + \cos(B - A)}{\sin(B - A) + \cos(B + A)}$Using the identities $\cos 	heta = \sin(90^\circ - 	heta)$:$E = \frac{\sin(B + A) + \sin(90^\circ - (B - A))}{\sin(B - A) + \sin(90^\circ - (B + A))}$$E = \frac{\sin(B + A) + \sin(90^\circ - B + A)}{\sin(B - A) + \sin(90^\circ - B - A)}$Using $\sin C + \sin D = 2 \sin(\frac{C+D}{2}) \cos(\frac{C-D}{2})$:Numerator: $\sin(B+A) + \sin(90^\circ - B + A) = 2 \sin(\frac{B+A+90^\circ-B+A}{2}) \cos(\frac{B+A-90^\circ+B-A}{2}) = 2 \sin(45^\circ + A) \cos(B - 45^\circ)$Denominator: $\sin(B-A) + \sin(90^\circ - B - A) = 2 \sin(\frac{B-A+90^\circ-B-A}{2}) \cos(\frac{B-A-90^\circ+B+A}{2}) = 2 \sin(45^\circ - A) \cos(B - 45^\circ)$$E = \frac{2 \sin(45^\circ + A) \cos(B - 45^\circ)}{2 \sin(45^\circ - A) \cos(B - 45^\circ)} = \frac{\sin(45^\circ + A)}{\sin(45^\circ - A)}$Using $\sin(x \pm y) = \sin x \cos y \pm \cos x \sin y$:$E = \frac{\sin 45^\circ \cos A + \cos 45^\circ \sin A}{\sin 45^\circ \cos A - \cos 45^\circ \sin A} = \frac{\frac{1}{\sqrt{2}} \cos A + \frac{1}{\sqrt{2}} \sin A}{\frac{1}{\sqrt{2}} \cos A - \frac{1}{\sqrt{2}} \sin A} = \frac{\cos A + \sin A}{\cos A - \sin A}$.

$\frac{\sin(B + A) + \cos(B - A)}{\sin(B - A) + \cos(B + A)} = $

Similar Questions

$\frac{\sin A+\sin 7 A+\sin 13 A}{\cos A+\cos 7 A+\cos 13 A} =$

If $\cos (A-B)=3/5$ and $\tan A \tan B=2$,then which one of the following is true?

$\cos ^4 \frac{\pi}{24} - \sin ^4 \frac{\pi}{24} = $

$\frac{\cos 9^\circ + \sin 9^\circ}{\cos 9^\circ - \sin 9^\circ} = $

Evaluate: $\cos^2 48^\circ - \sin^2 12^\circ$

Vedclass Test Series

Exam Paper Generator

Online Exam Module