Question

The value of  sin100°cos40°−cos100°sin40°=
a)½
b) root 3 by 2
c) 1 by root 2
d) 1​

Answer 1

Explanation:

We know that sin(a)cos(b) - cos(a)sin(b) = sin(a-b)

sin100°.cos40° - cos100°.sin40° = sin(100-40)° = sin60° = √3/2

Answer:

sin100°.cos40° - cos100°.sin40° = b) root 3 by 2

Answer 2

Answer:

ᴄᴏᴍᴘᴏᴜɴᴅ ғᴏʀᴍᴜʟᴀs

ᴄᴏs(ᴀ+ʙ)=ᴄᴏs ᴀ.ᴄᴏs ʙ-sɪɴ ᴀ.sɪɴ ʙ

ᴄᴏs(ᴀ-ʙ)=ᴄᴏs ᴀ.ᴄᴏs ʙ+sɪɴ ᴀ.sɪɴ ʙ

sɪɴ(ᴀ+ʙ)=sɪɴ ᴀ.ᴄᴏs ʙ+ᴄᴏs ᴀ.sɪɴ ʙ

sɪɴ(ᴀ-ʙ)=sɪɴ ᴀ.ᴄᴏs ʙ-ᴄᴏs ᴀ.sɪɴ ʙ

ɴᴏᴡ ɪɴ ᴛʜɪs ǫᴜᴇsᴛɪᴏɴ ᴀᴘᴘʟʏɪɴɢ ᴛʜᴇsᴇ ғᴏʀᴍᴜʟᴀ (ʙʏ ᴄᴏs(ᴀ-ʙ) ғᴏʀᴍᴜʟᴀ)

ᴀ=100° & ʙ=40°

ᴄᴏs 100°.ᴄᴏs 40° + sɪɴ 100° .sɪɴ 40° =ᴄᴏs(100°-40°)

……………..”””””””””………………….=ᴄᴏs(60°)

ᴀɴᴅ ᴠᴀʟᴜᴇ ᴏғ ᴄᴏs(60°)=1/2=0.5

ʜᴇɴᴄᴇ

ᴄᴏs100°.ᴄᴏs40°+sɪɴ100°.sɪɴ40° = 1/2