Question

4 cot² 0 - 4 cosec²0= ?

0 is considered as theta or x

Answer 1

QUESTION:

4cot²θ - 4cosec² = ?

USED FORMULAS:

sin²θ + cos²θ = 1

sin²θ = 1 - cos²θ

cotθ = sinθ/cosθ

cosecθ = 1/sinθ

ANSWER:

METHOD 1:

$4( { \frac{ \cos( \theta) }{ \sin( \theta) } )}^{2} - 4( { \frac{1}{ \sin( \theta) }) }^{2} \\ \\ = 4( \frac{ { \cos }^{2}( \theta) }{ { \sin}^{2}( \theta) } - \frac{1}{ { \sin }^{2} ( \theta)} ) \\ \\ = 4( \frac{ { \cos}^{2} ( \theta) - 1}{ { \sin}^{2}( \theta) } )$

$= - 4( \frac{1 - { \cos }^{2}( \theta) }{ { \sin}^{2} ( \theta)} ) \\ \\ = - 4( \frac{ { \sin}^{2} ( \theta)}{ { \sin }^{2} ( \theta)} ) \\ \\ = - 4$

METHOD 2:

formulas:

cot²θ = cosec²θ - 1

Answer:

= - 4(cot²θ - cosec²θ)

= - 4[(cosec² - 1) - cosec²)

= - 4( - cosec² + 1 + cosec²)

= - 4(1)

= - 4

CONCEPTS USED:

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