Question

alpha+ beta=90,show that √cos alpha×cosec beta-cos alpha sin beta=sin alpha

Answer 1

ʜᴇʏᴀ!!

ʜᴇʀᴇ's ʏᴏᴜʀ ᴀɴsᴡᴇʀ

_____________________

ɢɪᴠᴇɴ , 

ᴀʟᴘʜᴀ + ʙᴇᴛᴀ = 90°

==> ᴀʟᴘʜᴀ = ( 90° - ʙᴇᴛᴀ ) ------ ( ɪ ) 

==> ʙᴇᴛᴀ = ( 90° - ᴀʟᴘʜᴀ ) ----- ( ɪɪ )

ᴛᴏ ᴘʀᴏᴠᴇ , √ ( ᴄᴏs ᴀʟᴘʜᴀ × ᴄᴏsᴇᴄ ʙᴇᴛᴀ - ᴄᴏs ᴀʟᴘʜᴀ sɪɴ ʙᴇᴛᴀ ) = sɪɴ ᴀʟᴘʜᴀ.

ɴᴏᴡ ,   ʟ.ʜ.s
           -----------

√ ( ᴄᴏs ᴀʟᴘʜᴀ × ᴄᴏsᴇᴄ ʙᴇᴛᴀ - ᴄᴏs ᴀʟᴘʜᴀ sɪɴ ʙᴇᴛᴀ )

= √ { ᴄᴏs ( 90° - ʙᴇᴛᴀ ) × 1 / sɪɴ ʙᴇᴛᴀ - ᴄᴏs ( 90° - ʙᴇᴛᴀ ) × sɪɴ ʙᴇᴛᴀ } [ ★ ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴇϙᴜᴀᴛɪᴏɴ ( ɪ ) ]

= √ { sɪɴ ʙᴇᴛᴀ × 1 / sɪɴ ʙᴇᴛᴀ - sɪɴ ʙᴇᴛᴀ × sɪɴ ʙᴇᴛᴀ }

= √ ( 1 - sɪɴ^2 ʙᴇᴛᴀ )

= √ ᴄᴏs^2 ʙᴇᴛᴀ [ °•° ᴡᴇ ᴋɴᴏᴡ , sɪɴ^2 ʙᴇᴛᴀ + ᴄᴏs^2 ʙᴇᴛᴀ = 1 ]

= ᴄᴏs ʙᴇᴛᴀ

= ᴄᴏs ( 90° - ᴀʟᴘʜᴀ ) [ ★ ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴇϙᴜᴀᴛɪᴏɴ ( ɪɪ ) ]

= sɪɴ ᴀʟᴘʜᴀ

ᴀɴᴅ , ʀ.ʜ.s = sɪɴ ᴀʟᴘʜᴀ
         ---------
★ sᴏ , ʟ.ʜ.s = ʀ.ʜ.s [ ʜᴇɴᴄᴇ ᴘʀᴏᴠᴇᴅ ]

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ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ ᴅᴇᴀʀ! :)

★ ᴅᴇᴠɪʟ ᴋɪɴɢ

Answer 2

Answer:

answer in attachment

Explanation: