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$\mathsf{sin({\dfrac{\pi}{2}} + \: \theta). \cot( \pi - \theta). \cot({ \dfrac{3\pi}{2}}+ { \theta})} =$


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Answer 1

$sin(\frac{\pi}{2}+\theta)\times cot(\pi-\theta)\times cot(\frac{3 \pi}{2}+\theta)$

$\implies sin(90+\theta)\times cot(180-\theta) \times cot(270+\theta)$

$\implies cos\theta \times -cot \theta \times -tan \theta$

$\implies cos \theta \times cot\theta \times tan \theta$

$\implies cos \theta \times 1$

$\implies cos \theta$

The value is $\mathsf {cos\: \theta}$

FORMULAS USED :

$sin(90+\theta)=cos\theta$

$cot(\frac{3\pi}{2}-\theta)=-tan\theta$

$cot(\pi-\theta)=-cot\theta$

$cot\theta\times tan\theta=1$

Hope it helps :-)

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Answer 2

Answer:

cosθ

Step-by-step explanation:

Important Formulas:

(i) sin(90 + θ) = cosθ

(ii) cot(90 - θ) = tanθ

(iii) cot(2Π - θ) = -cotθ

Now,

Given Equation is sin(π/2 + θ) * cot(π/2 - θ) * cot(3π/2 + θ)

Putting π = 180°.

= sin[90 + θ] * cot[180 - θ] * cot[270 + θ]

= cosθ * -cotθ * cot[360° - 90° + θ]

= cosθ * -cotθ * cot[360° - (90 - θ)]

= cosθ * -cotθ * cot[2π - (90 - θ)]

= cosθ * -cotθ * -cot[90 - θ]

= cosθ * -cotθ * -tanθ

= cosθ * cotθ * tanθ

= cosθ * cotθ * (1/cotθ)

= cosθ.

Hope it helps!