Question

evaluate the following expression

Answer 1

ꜱᴄɪᴇɴᴄᴇ, ᴀɴʏ ꜱʏꜱᴛᴇᴍ ᴏꜰ ᴋɴᴏᴡʟᴇᴅɢᴇ ᴛʜᴀᴛ ɪꜱ ᴄᴏɴᴄᴇʀɴᴇᴅ ᴡɪᴛʜ ᴛʜᴇ ᴘʜʏꜱɪᴄᴀʟ ᴡᴏʀʟᴅ ᴀɴᴅ ɪᴛꜱ ᴘʜᴇɴᴏᴍᴇɴᴀ ᴀɴᴅ ᴛʜᴀᴛ ᴇɴᴛᴀɪʟꜱ ᴜɴʙɪᴀꜱᴇᴅ ᴏʙꜱᴇʀᴠᴀᴛɪᴏɴꜱ ᴀɴᴅ ꜱʏꜱᴛᴇᴍᴀᴛɪᴄ ᴇxᴘᴇʀɪᴍᴇɴᴛᴀᴛɪᴏɴ. ɪɴ ɢᴇɴᴇʀᴀʟ, ᴀ ꜱᴄɪᴇɴᴄᴇ ɪɴᴠᴏʟᴠᴇꜱ ᴀ ᴘᴜʀꜱᴜɪᴛ ᴏꜰ ᴋɴᴏᴡʟᴇᴅɢᴇ ᴄᴏᴠᴇʀɪɴɢ ɢᴇɴᴇʀᴀʟ ᴛʀᴜᴛʜꜱ ᴏʀ ᴛʜᴇ ᴏᴘᴇʀᴀᴛɪᴏɴꜱ ᴏꜰ ꜰᴜɴᴅᴀᴍᴇɴᴛᴀʟ ʟᴀᴡꜱ. ꜱᴄɪᴇɴᴄᴇ

Answer 2

Answer:

$sinx$ [option B]

Step-by-step explanation:

$2tan(x/2) / (1 + tan^{2}(x/2))$

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$sec^{2}(x/2) - tan^{2}(x/2) = 1\\\\1 + tan^{2}(x/2) = sec^{2}(x/2)$

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Substitute:

$2tan(x/2) / (1 + tan^{2}(x/2))$ = $2tan(x/2) / sec^{2}(x/2) = 2tan(x/2) * cos^{2}(x/2) = 2[sin(x/2) / cos(x/2)] * cos^{2}(x/2)$

= $2sin(x/2) * cos(x/2) = sin(x)$       [ Since 2sinacosa = sin(2a) ]

Hence sin(x) is the answer.

Hope it helps!