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Questions
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
Prove that: tan θ + cot θ = sec θ cosec θ
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Solution
L.H.S. = cot θ + tan θ
L.H.S. = `costheta/sintheta + sintheta/costheta`
L.H.S. = `(cos^2theta + sin^2theta)/(sintheta costheta)`
[cos2 θ + sin2 θ = 1]
L.H.S. = `1/(sintheta costheta)`
Use Reciprocal Identities:
The expression can be split into `(1/sin θ) xx (1/cos θ)`.
`1/sin θ` = cosec θ
`1/cos θ` = sec θ
L.H.S. = cosec θ.sec θ
L.H.S. = sec θ.cosec θ
∴ L.H.S. = R.H.S.
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Activity:
L.H.S. = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` ...`[sin^2"A" + square = 1]`
= `square` – cos2A ...[sin2A = 1 – cos2A]
= `square`
= R.H.S.
