If x = cosec A + cos A and y = cosec A - cos A then prove that
[tex]( \frac{2}{x + y} ) {}^{2} + ( \frac{x - y}{2} ) {}^{2} = 1[/tex]
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If x = cosec A + cos A and y = cosec A - cos A then prove that
[tex]( \frac{2}{x + y} ) {}^{2} + ( \frac{x - y}{2} ) {}^{2} = 1[/tex]
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Step-by-step explanation:
Given:-
⇒x=cosecA+cosA
⇒y=cosecA−cosA
To prove:-
⇒(
x+y
2
)
2
+(
2
x−y
)
2
−1=0
∴x+y=cosecA+cosA+cosecA−cosA=2cosecA
x−y=cosecA+cosA−cosecA+cosA=2cosA
∴(
x+y
2
)
2
+(
2
x−y
)
2
−1=(
2cosecA
2
)
2
+(
2
2cosA
)
2
−1
⇒(sinA)
2
+(cosA)
2
−1
⇒sin
2
A+cos
2
A−1
⇒1−1
⇒0
Hence proved.