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