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Question
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
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Solution
We have ,
`sqrt(3) sin theta = cos theta`
⇒ `sin theta/ cos theta = 1/ sqrt(3)`
⇒ `tan theta = 1/ sqrt(3)`
⇒ `tan theta = tan 30°`
∴ `theta = 30°`
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Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
