If A, B, C, D are the angles of a cyclic quad | vedclass

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

Question

(A) In a cyclic quadrilateral,the sum of opposite angles is $180^{\circ}$. Thus,$A + C = 180^{\circ}$ and $B + D = 180^{\circ}$.Using trigonometric id

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) In a cyclic quadrilateral,the sum of opposite angles is $180^{\circ}$. Thus,$A + C = 180^{\circ}$ and $B + D = 180^{\circ}$.Using trigonometric identities:$\cos(180^{\circ} + A) = -\cos A$$\cos(180^{\circ} - B) = -\cos B$$\cos(180^{\circ} - C) = -\cos C$$\sin(90^{\circ} - D) = \cos D$Substituting these into the expression:$-\cos A - \cos B - \cos C - \cos D = -(\cos A + \cos C) - (\cos B + \cos D)$Since $C = 180^{\circ} - A$,$\cos C = \cos(180^{\circ} - A) = -\cos A$,so $\cos A + \cos C = 0$.Similarly,$D = 180^{\circ} - B$,$\cos D = \cos(180^{\circ} - B) = -\cos B$,so $\cos B + \cos D = 0$.Therefore,the expression equals $-(0) - (0) = 0$.

If $A, B, C, D$ are the angles of a cyclic quadrilateral taken in order,then $\cos(180^{\circ} + A) + \cos(180^{\circ} - B) + \cos(180^{\circ} - C) - \sin(90^{\circ} - D) =$

Similar Questions

Convert $6$ radians into degree measure.

If $\theta$ lies in the first quadrant and $5 \tan \theta = 4$,then $\frac{5 \sin \theta - 3 \cos \theta}{\sin \theta + 2 \cos \theta}$ is equal to

Find the values of the other five trigonometric functions if $\tan x = -\frac{5}{12}$ and $x$ lies in the second quadrant.

$\sin 15^\circ + \cos 105^\circ = $

If $\cosh x = \frac{\sqrt{14}}{3}$,$\sinh x = \cos \theta$ and $-\pi < \theta < -\frac{\pi}{2}$,then $\sin \theta =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module