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Question
If sec θ = `25/7`, then find the value of tan θ.
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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L.H.S = `square`
= `square (1 - (sin^2theta)/(tan^2theta))`
= `tan^2theta (1 - square/((sin^2theta)/(cos^2theta)))`
= `tan^2theta (1 - (sin^2theta)/1 xx (cos^2theta)/square)`
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= R.H.S
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