Question

Prove that cotA- cosA/ cotA+ cosA = cosecA- 1/ cosecA+1

Answer 1

Lhs = (cotA - cosA)/(cotA+cosA)

=(cosA/sinA - cosA)/(cosA/sinA + cosA)

=cosA(1/sinA - 1)/cosA(1/sinA + 1)

= (1/sinA -1)/(1/sinA+1)

=(cosecA-1)/(cosecA+1) since 1/sinA= cosecA

=rhs

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Answer 2

Lhs= cotA-cosA/cotA+cos A

CosA/sin A-cosA/cosA /sin A+cosA

= we take lcm

Then we get

CosA -cosAsinA/sinA/cosA + cosAsinA/sinA

Cut sinA with sinA

So we get cosA-cosAsinA/cosA+cosAsinA

we take common so we get

CosA(1-sinA)/cosA(1+sinA)

Cut cosA with Cos A

1-sinA/ 1+sinA

devide numerator and denominator with sin A

1/sinA-sinA/sinA /1/sinA+ sinA/sinA

(1/sinA = cosecA)

then we get cosecA - 1/cosecA+1

hope it helps you

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