If sin y = x sin (a + y) and d y d x = A 1 + x 2 − 2 x c o s a ′ , then the value of A is Options: A . &nbsp2 B . &nbspcos a C . &nbspsin a D . &nbspNone of these

Answer: Option C : C x = s i n y s i n ( a + y ) . . . . . ( i ) ⇒ d x d y = s i n ( a ) s i n 2 ( a + y ) ∴ d y d x = s i n 2 ( a + y ) s i n ( a ) = A 1 + x 2 − 2 x c o s a P u t x = 0 , y = 0 , t h e n A = s i n a

If sin y = x sin (a + y) and dydx=A1+x2−2xcos a′, then the va

Question

If sin y = x sin (a + y) and

\frac{d y}{d x} = \frac{A}{1 + x^{2} - 2 x c o s a^{'}},

then the value of A is

Options:

A . 2

B . cos a

C . sin a

D . None of these

Answer: Option C
:
C

x = \frac{s i n y}{s i n (a + y)} . . . . . (i)

\Rightarrow \frac{d x}{d y} = \frac{s i n (a)}{s i n^{2} (a + y)}

∴ \frac{d y}{d x} = \frac{s i n^{2} (a + y)}{s i n (a)} = \frac{A}{1 + x^{2} - 2 x c o s a}

P u t x = 0, y = 0,

t h e n A = s i n a

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