Question

plz send full solution​

Answer 1

Answer:

(I am considering theta as x)

(sinx +1-cosx)/(sinx-1+cosx)=(1+sinx)/(cosx)

taking Lhs

(2sin(x/2)cos(x/2)+1-1+2sin²(x/2)/(2sin(x/2)cos(x/2)-1+1-2sin²(x/2)

(sin(x/2)cos(x/2)+sin²(x/2))/(sin(x/2)cos(x/2)-sin²(x/2))

(cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2))

now rationalising -

(cos(x/2)+sin(x/2))²/(cos²(x/2)-sin²(x/2))

(1+2sin(x/2)cos(x/2))/(cos2(x/2))

(1+sin2(x/2))/(cosx)

(1+sinx)/(cosx) =R. H. S

hence proved.