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Question
If tan θ = `12/5`, then 5 sin θ – 12 cos θ = ?
Options
`119/13`
0
1
`1/13`
Solution
0
Explanation:
Here, tan θ = `12/5`
Now, according to Pythagoras theorem,
AC2 = AB2 + BC2
AC2 = 122 + 52
⇒ AC2 = 144 + 25
⇒ AC2 = 169
⇒ AC = 13
Hence, sin θ = `(AB)/(AC) = 12/13`
And cos θ = `(BC)/(AC) = 5/13`
So, 5 sin θ – 12 cos θ
= `5 xx 12/13 - 12 xx 5/13`
= `60/13 - 60/13`
= 0
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