Question

1 + sin 2A + cos 2A upon 1 1 + sin 2A - cos 2 is equal to COT A prove that ​

Answer 1

Answer:

The correct question is =

1+sin2A+Cos2A upon 1+sin2A-cos2A is equal to COT A.

Consider,

1+sin(2A)+cos(2A)1+sin(2A)−cos(2A)

=sin2(A)+cos2(A)+sin(2A)+cos(2A)sin2(A)+cos2(A)+sin(2A)−cos(2A) [Since, sin2(A)+cos2(A)=1]

=sin2(A)+cos2(A)+2sin(A)cos(A)+cos(2A)sin2(A)+cos2(A)+2sin(A)cos(A)−cos(2A) [Since, sin(2A)=2sin(A)cos(A)]

=sin2(A)+cos2(A)+2sin(A)cos(A)+cos2(A)−sin2(A)sin2(A)+cos2(A)+2sin(A)cos(A)−[cos2(A)−sin2(A)] [Since, cos(2A)=cos2(A)−sin2(A)]

=sin2(A)+cos2(A)+2sin(A)cos(A)+cos2(A)−sin2(A)sin2(A)+cos2(A)+2sin(A)cos(A)−cos2(A)+sin2(A)=2cos2(A)+2sin(A)cos(A)2sin2(A)+2sin(A)cos(A)=cos(A)sin(A)[cos(A)+sin(A)sin(A)+cos(A)]=cos(A)sin(A)=cot(A).

HENCE PROVED...