Question

why (Sin)(cos)=1, (cos)(sec)=1, and (tan)(cot)=1 ???

Answer 1

sinθ1−cosθ+tanθ1+cosθ

= sinθ(1+cosθ)(1−cosθ)(1+cosθ)+tanθ(1−cosθ)(1+cosθ)(1−cosθ)

= sinθ(1+cosθ)1−cos2θ+tanθ(1−cosθ)1−cos2θ

= sinθ(1+cosθ)sin2θ+sinθ(1−cosθ)cosθsin2θ

= 1+cosθsinθ+1−cosθcosθsinθ

= 1sinθ+cosθsinθ+1cosθsinθ−1sinθ

= cscθ+cotθ+secθcscθ−cscθ

= secθcscθ+cotθ

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Answer 2

=sin* cos
=sin*1/sin[cos=1/sin]
=1[sin will get cancelled]

=cos*sec
=cos*1/cos
=1

=tan*cot
=tan*1/tan
=1

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