prove that (SinA+CosA) (SecA+CosecA)=2SecA.CosecA
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(sᴇᴄA+ᴄᴏsᴇᴄA)(sɪɴA+ᴄᴏsA)=+sᴇᴄA.ᴄᴏsᴇᴄA.
Cᴏɴsɪᴅᴇʀ LHS
(sᴇᴄA+ᴄᴏsᴇᴄA)(sɪɴA+ᴄᴏsA)
=sᴇᴄA(sɪɴA+ᴄᴏsA)+ᴄᴏsᴇᴄA(sɪɴA+ᴄᴏsA)
=sᴇᴄA.sɪɴA+sᴇᴄA.ᴄᴏsA+ᴄᴏsᴇᴄA.sɪɴA+ᴄᴏsᴇᴄA.ᴄᴏsA
(As ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ sᴇᴄA.ᴄᴏsA= ᴀɴᴅ ᴄᴏsᴇᴄA.sɪɴA=)
=sɪɴA.sᴇᴄA+++ᴄᴏsᴇᴄA.ᴄᴏsA
=sɪɴA./ᴄᴏsA++ᴄᴏsA./sɪɴA
=+ᴛᴀɴA+ᴄᴏᴛA
=+sɪɴA/ᴄᴏsA+ᴄᴏsA/sɪɴA.
=+(sɪɴ²A+ᴄᴏs²A)/ᴄᴏsA.sɪɴA
(As ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ sɪɴ²A+ᴄᴏs²A=)
=+/ᴄᴏsA.sɪɴA
Bᴜᴛ ᴡᴋᴛ /sɪɴA=ᴄᴏsᴇᴄA ᴀɴᴅ /ᴄᴏsᴄᴇA
Tʜᴇʀᴇғᴏʀᴇ LHS=+sᴇᴄA.ᴄᴏsᴇᴄA.
Hᴇɴᴄᴇ LHS=RHS
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