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Trigonometric Ratios

Prove the fol...

Question

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

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Solution

(i)

(ii)

(iii)

$= \frac{\sin^{2} θ}{\cos θ (\sin θ - \cos θ)} - \frac{\cos^{2} θ}{\sin θ (\sin θ - \cos θ)}$

= secθ cosec θ +

= R.H.S.

(iv)

= R.H.S

(v)

Using the identity cosec² = 1 + cot²,

L.H.S =

= cosec A + cot A

= R.H.S

(vi)

(vii)

(viii)

(ix)

Hence, L.H.S = R.H.S

(x)

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