Question

if sin B=1/2. show that 3cpsB-4cos^3 B =0

Answer 1

first you apply pythagorus theorem to know the value of cosB .then solve it

Answer 2

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✒ ᴡᴇ ʜᴀᴠᴇ,

sɪɴ ʙ = ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ/ʜʏᴘᴏᴛᴇɴᴜsᴇ = 1/2

sᴏ, ᴡᴇ ᴅʀᴀᴡ ᴀ ʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇ ᴀʙᴄ, ʀɪɢʜᴛ ᴀɴɢʟᴇᴅ ᴀᴛ ᴄ sᴜᴄʜ ᴛʜᴀᴛ

ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ = ᴀᴄ = 1 ᴜɴɪᴛ, ʜʏᴘᴏᴛᴇɴᴜsᴇ = ᴀʙ = 2 ᴜɴɪᴛs.

ᴀᴘᴘʟʏɪɴɢ ᴘʏᴛʜᴀɢᴏʀᴀs ᴛʜᴇᴏʀᴇᴍ ɪɴ ʙᴄᴀ, ᴡᴇ ᴏʙᴛᴀɪɴ

ᴀʙ² = ʙᴄ² + ᴀᴄ²

=> 2² = ʙᴄ² + 1

=> ʙᴄ² = 3

=> ʙᴄ = √3

ᴛʜᴇʀᴇғᴏʀᴇ,

ᴄᴏs ʙ = ʙᴄ/ᴀʙ = √3/2

ɴᴏᴡ,

3 ᴄᴏs ʙ - 4 ᴄᴏs³ ʙ = 3 × √3/2 - 4 [√3/2]³

= 3√3/2 - 4 × 3√3/8

= 3√3/2 - 3√3/2

= 0

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