Question

Cos A minus Sin A + one upon Cos A + Sin A minus 1 is equal to cosec A + cot a using the identity Kaushik square is equal to one plus cot squared

Answer 1

here is ur answer

hope u understand it .....

Answer 2

Answer:

Step-by-step explanation:

we have to prove ( cosA - sinA + 1 ) / ( cosA + sinA - 1 ) =  cosecA + cotA

left hand side = ( cosA - sinA + 1 ) / ( cosA + sinA - 1 )

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

= ( sinA cosA - sin²A + sinA ) / sinA ( cosA + sinA - 1 )

= [ sinA cosA + sinA - ( 1 - cos²A ) ] / sinA ( cosA + sinA - 1 )

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

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

= ( 1 + cosA ) / sinA

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

= cosecA + cot A

then  (cosA - sinA + 1 ) / ( cosA + sinA - 1 ) =  cosecA + cotA (proved)