(1+ cot A - cosec A) (1+ tan A + sec A) = 2

(1+cot A -cosec A)(1+ tan A + sec A)

Lhs

=(1 +cos A/sin A - 1/sin A)(1 + sin A/cos A +1/cos A)

=(sin A+cos A -1/sin A)(cos A +sin A+1/cos A)

=(sin A+cos A -1)(sin A+cos A+1)/sin Acos A

=[(sin A+cos A)2-(1)2]/sin Acos A

=[sin2A+cos2A +2sin Acos A - 1]/sin Acos A

=[1-1+2sin Acos A]/sin Acos A

=2sin Acos A/sin Acos A

=2 =Rhs

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(1 + cot A - cosec A ) (1 + tan A + sec A ) = 2

L.H.S. = (1 + cos A/sin A - 1/sin A ) (1 + sin A/cos A + 1 / cos A ) { CONVERTING } 

L.H.S. = (sin A + cos A - 1 / sin A ) (cos A + sin A +1 / cos A ) 

L.H.S. = (sin A + cos A )²  - (1)² / sin Acos A  { MULTIPLYING USING IDENTITY }

L.H.S. = (sin²A + cos²A) + 2sin Acos A - 1 / sin Acos A

L.H.S. = 1 + 2sin Acos A -1 / sin Acos A

L.H.S. = 2sin Acos A / sin Acos A

L.H.S. = 2

Hence, L.H.S = R.H.S 

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