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Question
If sec θ = `25/7`, then find the value of tan θ.
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Solution
∵ sec2θ – tan2θ = 1 ......[Identities]
`(25/7)^2 - ("tan" theta)^2 = 1`
`625/49 -1 = ("tan" theta)^2`
`(625 - 49)/49 = ("tan" theta)^2`
`576/49 = ("tan" theta)^2`
`"tan" theta = 24/7`
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Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
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= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
