Question

if A,B,C,D are angles of a cyclic quadrilateral ,then prove that (a)sinA-sinC=sinD-SinB and (B)cos A+cos B = cos C+cos D.​

Answer 1

Answer:

If A, B, C, D are angles of a cyclic quadrilateral then, A + C = B + D = 180° ........(1)

i. sinA - sinC = sinD - sinB

LHS = sinA - sinC

= sin(180° - C) - sinC [ from equation (1), ]

= sinC - sinC = 0

RHS = sinD - sinB

= sin(180° - B) - sinB [ from equation (1)]

= sinB - sinB = 0

hence, LHS = RHS

ii. LHS = cosA + cosB + cosC + cosD

= cosA + cos(180° - A) + cosC + cos(180° - C) [ from equation (1), ]

= cosA - cosA + cosC - cosC

= 0 + 0 = 0 = RHS

Step-by-step explanation:

Answer 2

Answer:

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Step-by-step explanation:

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