Question

if sec theta + tan theta = p then find the value of tan theta ?

Answer 1

Answer: (p2 – 1)/2p

Solution:

Given,

sec θ + tan θ = p….(i)

We know that,

sec2θ – tan2θ = 1

(sec θ + tan θ)(sec θ – tan θ) = 1

p(sec θ – tan θ) = 1

sec θ – tan θ = 1/p….(ii)

Subtracting (ii) from (i),

sec θ + tan θ – sec θ + tan θ = p – (1/p)

2 tan θ = (p2 – 1)/p

tan θ = (p2 – 1)/2p

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Answer 2

Step-by-step explanation:

✍︎ANSWER✍️

sᴄɪᴇɴᴄᴇ, ᴀɴʏ sʏsᴛᴇᴍ ᴏғ ᴋɴᴏᴡʟᴇᴅɢᴇ ᴛʜᴀᴛ ɪs ᴄᴏɴᴄᴇʀɴᴇᴅ ᴡɪᴛʜ ᴛʜᴇ ᴘʜʏsɪᴄᴀʟ ᴡᴏʀʟᴅ ᴀɴᴅ ɪᴛs ᴘʜᴇɴᴏᴍᴇɴᴀ ᴀɴᴅ ᴛʜᴀᴛ ᴇɴᴛᴀɪʟs ᴜɴʙɪᴀsᴇᴅ ᴏʙsᴇʀᴠᴀᴛɪᴏɴs ᴀɴᴅ sʏsᴛᴇᴍᴀᴛɪᴄ ᴇxᴘᴇʀɪᴍᴇɴᴛᴀᴛɪᴏɴ. ... ɪɴ ɢᴇɴᴇʀᴀʟ, ᴀ sᴄɪᴇɴᴄᴇ ɪɴᴠᴏʟᴠᴇs ᴀ ᴘᴜʀsᴜɪᴛ ᴏғ ᴋɴᴏᴡʟᴇᴅɢᴇ ᴄᴏᴠᴇʀɪɴɢ ɢᴇɴᴇʀᴀʟ ᴛʀᴜᴛʜs ᴏʀ ᴛʜᴇ ᴏᴘᴇʀᴀᴛɪᴏɴs ᴏғ ғᴜɴᴅᴀᴍᴇɴᴛᴀʟ ʟᴀᴡs.

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σкαy i ωiℓℓ...✰✰

Answer: (p2 – 1)/2p

Solution:

Given,

sec θ + tan θ = p….(i)

We know that,

sec2θ – tan2θ = 1

(sec θ + tan θ)(sec θ – tan θ) = 1

p(sec θ – tan θ) = 1

sec θ – tan θ = 1/p….(ii)

Subtracting (ii) from (i),

sec θ + tan θ – sec θ + tan θ = p – (1/p)

2 tan θ = (p2 – 1)/p

tan θ = (p2 – 1)/2p

✦ ✧ ✦ ✧ ✦ ✧✦ ✧ ✦ ✧ ✦

hope this helps you!!