Question

34. If x= cosec A+ cos A and y=cosec A-cos A then prove that (2/x+y) square+(x-y/2)square - 1 = 0​

Answer 1

Answer:

Step-by-step explanation:

SOLVING LHS

[2/(cosecA+cosA+cosecA-cosA)]²+[cosecA+cosA-(cosecA-cosA)/2]²-1

eliminate values of cosA and cosec A from the above given eqn.

[2/2cosecA]²+[2cosA/2]²-1

eliminate value of 2 from above eqn

[1/cosecA]²+[cosA]²-1              [1/cosecA=sinA]

transfer value of cosecA to numerator

sin²A+cos²A-1                     [sin²A+cos²A=1]

put trignometric identity

1-1=0

∴LHS=RHS

hence proved