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

(D) Given that $ABCD$ is a cyclic quadrilateral.In a cyclic quadrilateral,the sum of opposite angles is $180^\circ$.Therefore,$A + C = 180^\circ$ and

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(D) Given that $ABCD$ is a cyclic quadrilateral.In a cyclic quadrilateral,the sum of opposite angles is $180^\circ$.Therefore,$A + C = 180^\circ$ and $B + D = 180^\circ$.From $A + C = 180^\circ$,we get $A = 180^\circ - C$.Taking cosine on both sides,$\cos A = \cos(180^\circ - C) = -\cos C$.This implies $\cos A + \cos C = 0$.Similarly,from $B + D = 180^\circ$,we get $B = 180^\circ - D$.Taking cosine on both sides,$\cos B = \cos(180^\circ - D) = -\cos D$.This implies $\cos B + \cos D = 0$.Adding these two equations,we get $\cos A + \cos B + \cos C + \cos D = 0 + 0 = 0$.

If $A, B, C, D$ are the angles of a cyclic quadrilateral,then $\cos A + \cos B + \cos C + \cos D = $

Similar Questions

The minimum value of $(8 \sec^2 \theta + 2 \cos^2 \theta)$ is equal to :-

If $\sin^2 \theta = \frac{x^2 + y^2 + 1}{2x}$,then $x$ must be

The value of $\sec ^{2} \theta - \frac{\sin ^{2} \theta - 2 \sin ^{4} \theta}{2 \cos ^{4} \theta - \cos ^{2} \theta}$ is

The value of $x$ for the maximum value of $(\sqrt{3} \sin x + \cos x)$ is .....$^o$

If $x = \sin 130^\circ \cos 80^\circ$,$y = \sin 80^\circ \cos 130^\circ$,and $z = 1 + xy$,which one of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module