Question
Download Solution PDFThe value of \(\rm \left(\frac{1}{\sin \theta}+\frac{1}{\tan \theta}\right)\rm \left(\frac{1}{\sin \theta}-\frac{1}{\tan \theta}\right)\) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\rm \left(\frac{1}{\sin θ}+\frac{1}{\tan θ}\right)\rm \left(\frac{1}{\sin θ}-\frac{1}{\tan θ}\right)\)
Formula used:
(A2 - B2) = (A + B) × (A - B)
Cosec2 θ - cot2 θ = 1
Calculation:
\(\rm \left(\frac{1}{\sin θ}+\frac{1}{\tan θ}\right)\rm \left(\frac{1}{\sin θ}-\frac{1}{\tan θ}\right)\)
⇒ (cosec θ + cot θ) × (cosec θ - cot θ)
⇒ Cosec2 θ - cot2 θ
⇒ 1
∴ The correct answer is 1.
Last updated on Jun 13, 2025
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