Subject :IMO Class : Class 10
If sin θ + cos θ = a and 
, then ____.
, then ____.
(A)
(B)
(C) ab = b 2 - 1
(D) a + b = 1
Ans 1:
Class : Class 10
Answer is (A)
a=sin(A) + cos(A)........................................given as equation (1)
a^2=sin^2(A) + cos^2 (A) + 2 sin(A)cos(A)
a^2=1 + 2 sin(A)cos(A)
therefore,
sin(A)cos(A) = (a^2 - 1)/2..............................equation (2)
b = {sin(A) + cos(A)} / sin(A)cos(A)
b = a/a^2-1 x 2/1.............................................from equation (1) and (2)
therefore
b = 2a/a^2-1