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Integration as Antiderivative

52. prove tha...

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52. prove that sin(x+y)=sinx.cosy+cosx.siny

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x + y

being acute and if

sin x . cos y + cos x . sin y = 0

then the value of

sin x + sin y =

\frac{sin x - sin y}{cos x + cos y} = tan \frac{x - y}{2}

\frac{sin (x + y)}{sin (x - y)} = \frac{tan x + tan y}{tan x - tan y}

x, y \in [0, 2 π]

, then total number of ordered pairs

(x, y)

satisfying the equation

sin x . cos y = 1

0 \leq x \leq 3 π, 0 \leq y \leq 3 π

cos x . sin y = 1

, then the possible number of ordered pair

(x, y)

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