\(\rm \left(\frac{1}{\sin \theta}+\frac{1}{\tan \theta}\right)\rm \left(\frac{1}{\sin \theta}-\frac{1}{\tan \theta}\right)\) దీని విలువ ఎంత?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 2)

Answer 1

ఇచ్చింది:

\(\rm \left(\frac{1}{\sin θ}+\frac{1}{\tan θ}\right)\rm \left(\frac{1}{\sin θ}-\frac{1}{\tan θ}\right)\)

ఉపయోగించిన సూత్రము:

(A² - B²) = (A + B) × (A - B)

Cosec² θ - cot² θ = 1

గణన:

\(\rm \left(\frac{1}{\sin θ}+\frac{1}{\tan θ}\right)\rm \left(\frac{1}{\sin θ}-\frac{1}{\tan θ}\right)\)

⇒ (cosec θ + cot θ) × (cosec θ - cot θ)

⇒ Cosec2 θ - cot2 θ

⇒ 1

∴ సరైన సమాధానం 1.

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