Question

If cosec θ + cot θ = k. then prove that cos teta =k²-1/k²+1.

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer:-

Theta is taken as "A".

Given:

Cosec A + Cot A = k

→ (1/Sin A) + (Cos A/Sin A) = k

[ Cosec A = 1/Sin A ; Cot A = Cos A/Sin A ]

→ (1 + Cos A)/Sin A = k

Squaring both sides we get,

→ (1 + Cos A)²/Sin² A = k²

→ (1 + Cos A)(1 + Cos A)/(1 - Cos² A) = k²

[ Sin² A + Cos² A = 1 => Sin² A = 1 - Cos² A ]

→ (1 + Cos A)(1 + Cos A)/(1 + Cos A)(1 - Cos A) = k²

[ a² - b² = (a + b)(a - b) ]

→ (1 + Cos A)/(1 - Cos A) = k²

→ (1 + Cos A) = k²(1 - Cos A)

→ 1 + Cos A = k² - k² Cos A

→ Cos A + k² Cos A = k² - 1

→ Cos A (1 + k²) = k² - 1

→ Cos A = (k² - 1)/(1 + k²)

→ Cos A = (k² - 1)(k² + 1)

Hence, Proved.