Question

if ABCD is a cyclic quadrilateral then find the value of sinA+sinB-sinC-sinD

pls give proper answer with explanation

from chapter trigonometry class 11​

Answer 1

Answer:

0

Step-by-step explanation:

in a cyclic quadrilateral , opp angles sum is 180

A + C = 180 ....eqn 1

B + D = 180 ....eqn2

A = 180 - C

sinA = sin(180-C)

sinA = sinC

therefore, sin A - sinC = 0

similarly from eqn 2, we get

sinB - sinD = 0

LHS = sinA + Sin B - sinC -sinD

= (sinA - sinC)+ sin B -sinD

= 0

Answer 2

Step-by-step explanation:

sinA+sinB-sinC-sinD

sinA+sinB-sin(180-A)-sin(180-B)(by property of cyclic quadrilateral)

sinA+sinB-sinA-sinB=0

in a cyclic quadrlateral sum of opp angles is 180