What is the value of frac{[sin (y-z)+sin (y+z | vedclass

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

Question

(B) Given expression: $\frac{\sin (y-z)+\sin (y+z)+2 \sin y}{\sin (x-z)+\sin (x+z)+2 \sin x}$Using the trigonometric identity $\sin A + \sin B = 2 \si

Vedclass · Accepted Answer

$\frac{\sin y}{\sin x}$

Vedclass · Answer

(B) Given expression: $\frac{\sin (y-z)+\sin (y+z)+2 \sin y}{\sin (x-z)+\sin (x+z)+2 \sin x}$Using the trigonometric identity $\sin A + \sin B = 2 \sin \left( \frac{A+B}{2} \right) \cos \left( \frac{A-B}{2} \right)$:Numerator: $\sin (y-z) + \sin (y+z) + 2 \sin y = 2 \sin y \cos z + 2 \sin y = 2 \sin y (\cos z + 1)$Denominator: $\sin (x-z) + \sin (x+z) + 2 \sin x = 2 \sin x \cos z + 2 \sin x = 2 \sin x (\cos z + 1)$Dividing the numerator by the denominator:$= \frac{2 \sin y (\cos z + 1)}{2 \sin x (\cos z + 1)}$$= \frac{\sin y}{\sin x}$

What is the value of $\frac{[\sin (y-z)+\sin (y+z)+2 \sin y]}{[\sin (x-z)+\sin (x+z)+2 \sin x]} = ?$

Similar Questions

If $A, B, C$ are acute positive angles such that $A + B + C = \pi$ and $\cot A \cot B \cot C = K$,then

The value of $\frac{\sin 150^{\circ}-5 \cos 300^{\circ}+7 \tan 225^{\circ}}{\tan 135^{\circ}+3 \sin 210^{\circ}}$ is

If $m$ and $M$ are the minimum and the maximum values of $4 + \frac{1}{2} \sin^2 2x - 2 \cos^4 x$ for $x \in R$,then $M - m$ is equal to

The maximum value of the expression $E = \sin \theta + \cos \theta + \sin 2\theta$ is-

The value of $x$ that satisfies the relation $x = 1 - x + x^2 - x^3 + x^4 - x^5 + \dots \infty$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module