UPSC CDS 1 2022 Math Paper

Given:
A,B,C,D are the angles of a cyclic quadrilateral sin(‌

A+C

2

)+sin(‌

B+D

2

)
Concept used:
The sum of the opposite angles of a cyclic quadrilateral is supplementary. Calculation:
According to the concept,
∠A+∠C=180∘
&∠B+∠D=180∘
So,
sin(‌

A+C

2

)+sin(‌

B+D

2

)=sin(‌

180∘

2

)+sin(‌

180∘

2

)
⇒sin(‌

A+C

2

)+sin(‌

B+D

2

)=sin‌90∘+sin‌90∘
⇒sin(‌

A+C

2

)+sin(‌

B+D

2

)=1+1
⇒sin(‌

A+C

2

)+sin(‌

B+D

2

)=2
∴ Required answer is 2