Question

evalute the following question (1+tan+sec) 1+(cot-cosec)

Answer 1

☆☆ranshsangwan☆☆


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