Question

11. If tan 0 =
(cosec?0- sec0)
tz, show that
(cosec?0+ sec?0)
3
3
4​

Answer 1

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.