Question

$(1 + cot^{2})(1 - cos ^{2} )(1 + cos^{2} )$
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Answer 1

Answer:

$1 + { \cos( \alpha ) }^{2}$

Step-by-step explanation:

$(1 + { \cot( \alpha ) }^{2} )(1 - { \cos( \alpha ) }^{2} )(1 + { \cos( \alpha ) }^{2} ) \\ = { \csc( \alpha ) }^{2} \times { \sin( \alpha ) }^{2} (1 + { \cos( \alpha ) }^{2} ) \\ = 1 + { \cos( \alpha ) }^{2}$

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Answer 2

(1 + cot^2 (θ) )(1 - cos^2 (θ) )(1 + cos^2 (θ) )

= (1+cos^2 (θ) / sin^2 (θ) )(sin^2 (θ) )(1+cos^2 (θ) )

= (sin^2 (θ)+cos^2 (θ))(1+cos^2 (θ))

= 1 × (1+cos^2 (θ) )

= 1+cos^2 (θ)