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प्रश्न
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
उत्तर
LHS = cot θ - tan θ
= `cos θ/sin θ - sin θ/cos θ`
= `(cos^2 θ - sin^2 θ)/(sin θ. cos θ)`
= `(cos^2 θ - (1 - cos^2 θ))/(sin θ. cos θ)`
= `(2cos^2 θ - 1)/(sin θ. cos θ)`
= RHS
Hence proved.
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If sec θ = `25/7`, find the value of tan θ.
Solution:
1 + tan2 θ = sec2 θ
∴ 1 + tan2 θ = `(25/7)^square`
∴ tan2 θ = `625/49 - square`
= `(625 - 49)/49`
= `square/49`
∴ tan θ = `square/7` ........(by taking square roots)
