Question
Download Solution PDFFind the value of \(\frac{1-\cot ^2 \theta}{\tan ^2\theta-1}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\frac{1-\cot ^2 θ}{\tan ^2θ-1}\)
Formula Used:
Cotθ = Cosθ/Sinθ
Tanθ = Sinθ/Cosθ
Calculation:
\(\frac{1-\cot ^2 θ}{\tan ^2θ-1}\)
⇒ {1 - (Cosθ/Sinθ)2}/{(Sinθ/Cosθ)2 - 1)}
⇒ {(Sin2θ - Cos2θ )/Sin2θ /(Sin2θ - Cos2θ )/ Cos2θ)
⇒ Cos2θ/ Sin2θ
⇒ Cot2 θ
∴ The correct answer is cot2 θ.
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