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Question
If 3 sin θ = 4 cos θ, then sec θ = ?
Solution
3 sin θ = 4cos θ .....[Given]
∴ `(sintheta)/(costheta) = 4/3`
∴ tan θ = `4/3`
We know that,
1 + tan2θ = sec2θ
∴ `1 + (4/3)^2` = sec2θ
∴ `1 + 16/9` = sec2θ
∴ sec2θ = `(9 + 16)/9`
∴ sec2θ = `25/9`
∴ sec θ = `5/3` ......[Taking square root of both sides]
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