Question

Prove (sinA + 1 +cosA) ( sinA - 1 + cosA) × sec.cosec = 2

Answer 1

Answer:

do it sin inverse and cos inverse after them multiply by themselves

Answer 2

Answer:

2

Step-by-step explanation:

(Sin A+1+Cos A)(sin a-1+Cos A)× sec A . Cosec A

= [{(Sin A+Cos A)+1}×{(Sin A+Cos A)-1}]×sec A . Cosec A

We have (a+b)(a-b) = a²-b²

here let's consider Sin A+ CosA = a and 1=b

then

{(SinA+Cos A)²-1²}× sec A . Cosec A

=We have (a+b)² formula= a²+b²+2ab

={(Sin²A+ Cos²A+ 2SinACosA)-1}×sec A . Cosec A

We have Sin²A+ Cos²A=1

={(1+ 2SinACosA)-1}×sec A . Cosec A

= 2SinACosA×sec A . Cosec A

= 2SinACosA×(1÷SinACosA)

=2