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Question
Prove that `(sintheta + tantheta)/cos theta` = tan θ(1 + sec θ)
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Solution
L.H.S = `(sintheta + tantheta)/cos theta`
= `sintheta/costheta + tantheta/costheta`
= tan θ + tan θ sec θ
= tan θ(1 + sec θ)
= R.H.S
∴ `(sintheta + tantheta)/cos theta` = tan θ(1 + sec θ)
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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
