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Question
If tan θ = `x/y`, then cos θ is equal to ______.
Options
`x/sqrt(x^2 + y^2)`
`y/sqrt(x^2 + y^2)`
`x/sqrt(x^2 - y^2)`
`y/sqrt(x^2 - y^2)`
Solution
If tan θ = `x/y`, then cos θ is equal to `underlinebb(y/sqrt(x^2 + y^2))`.
Explanation:
Given, tan θ = `x/y` ...(i)
We know that
tan θ = `"Perpendicular (P)"/"Base (B)"` ...(ii)
By comparing equations (i) and (ii), we get
P = x, B = y
H2 = P2 + B2 ...(Pythagoras theorem)
H2 = x2 + y2
H = `sqrt(x^2 + y^2)`
Then cos θ = `B/H`
= `y/sqrt(x^2 + y^2)`
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