Question

Write the value of $cot^{2}\Theta-\frac{1}{sin^{2}\Theta }$.

Answer 1

Answer:

The value of cot² θ - 1/sin² θ is - 1.

Step-by-step explanation:

Given : cot² θ - 1/sin² θ

= cot² θ - (1/sinθ)²

= cot² θ - cosec²θ

[By using the identity, 1/sinθ = cosecθ ]

= - 1

[By using the identity , cot² θ - cosec² θ = - 1]

cot² θ - 1/sin² θ = - 1

Hence, the value of cot² θ - 1/sin² θ is - 1.

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Answer 2

$cot^{2}\Theta-\frac{1}{sin^{2}\Theta } \\ \\ = \frac{cos^{2}\Theta}{sin^{2}\Theta} - \frac{1}{sin^{2}\Theta } \\ \\ = \frac{cos^{2}\Theta - 1}{sin^{2}\Theta} \\ \\ = \frac{-sin^{2}\Theta}{sin^{2}\Theta} \\ \\ = -1$

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