Question

Prove that cotA+CosecA-1/CotA-CosecA+1=1+CosA/SinA

Answer 1

cosec A + cot A - 1 / cot A - cosec A + 1
we know that,cosec ² A - cot ² A = 1
substituting this in the numerator
cosec A + cot A -(cosec ² A - cot ² A) / (cot A - cosec A + 1)
x²-y²= (x+y)(x-y)
cosec A + cot A - (cosec A + cot A) (cosec A - cot A) / (cot A - cosec A + 1)
taking common
(cosec A + cot A)(1-cosec A + cot A) / (cot A - cosec A + 1)
cancelling like terms in numerator and denominator
we are left with cosec A + cot A
= 1/sin A + cos A/sin A
= (1+cos A) / sin A



Hope it helps....

Answer 2

Hey !!!

cotA + coseA - 1 / cotA - cosecA + 1

cotA+cosecA-( Cosec²A-cot²A )/cotA-cosecA +1

•°• Cosec²A-cot²A =1 ⏪

cotA + cosecA - 1(cosecA + cotA )(cosecA -CotA )
=----------------------------------------
cotA - cosecA +1

= (cotA + CosecA )(CosecA + cotA +1)
-----------------------------------------
cotA - cosecA +1

= cotA + cosecA

cosA /sinA + 1/sinA

= cosA + 1/ sinA = 1 + cosA/SinA RHS

here prooved .lhs = rhs

Hope it helps you!!!

@Rajukumar111@@