Question

if A+B=90° prove that secA cosecB-tanA cotB=1 and sec2A-cot2B=1

Answer 1

ʜᴇʏᴀ!!

ʜᴇʀᴇ's ʏᴏᴜʀ ᴀɴsᴡᴇʀ

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ɢɪᴠᴇɴ , ᴀ + ʙ = 90° 

ᴏʀ , ᴀ = ( 90° - ʙ )

ɴᴏᴡ ,

1.  sᴇᴄᴀ ᴄᴏsᴇᴄʙ-ᴛᴀɴᴀ ᴄᴏᴛʙ=1 

         ʟ.ʜ.s

• sᴇᴄᴀ ᴄᴏsᴇᴄʙ - ᴛᴀɴᴀ ᴄᴏᴛʙ

= sᴇᴄ ( 90° - ʙ ) ᴄᴏsᴇᴄʙ - ᴛᴀɴ ( 90° - ʙ ) ᴄᴏᴛʙ

= ᴄᴏsᴇᴄʙ ᴄᴏsᴇᴄʙ - ᴄᴏᴛʙ ᴄᴏᴛʙ

= ᴄᴏsᴇᴄ^2ʙ - ᴄᴏᴛ^2ʙ

= 1  

ʀ.ʜ.s = 1
 
•°• ʟ.ʜ.s = ʀ.ʜ.s. [ ᴘʀᴏᴠᴇᴅ ]

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2. sᴇᴄ2ᴀ-ᴄᴏᴛ2ʙ=1

         ʟ.ʜ.s

•  sᴇᴄ^2ᴀ - ᴄᴏᴛ^2ʙ

= sᴇᴄ^2 ( 90° - ʙ ) - ᴄᴏᴛ^2ʙ

= ᴄᴏsᴇᴄ^2ʙ - ᴄᴏᴛ^2ʙ

= 1

ʀ.ʜ.s = 1

sᴏ , ʟ.ʜ.s = ʀ.ʜ.s [ ᴘʀᴏᴠᴇᴅ ]

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