Q97 / 170 · Manipal (MET) 2016 · Mathematics

If $\sin A+\cos B=a$ and $\sin B+\cos A=b$, then $\sin (A+B)$ is equal to

A
$\frac{a^2+b^2}{2}$
B
$\frac{a^2-b^2+2}{2}$
Correct answer
C
$\frac{a^2+b^2-2}{2}$
D
None of these

Solution

On squaring and adding the given equations, we get $+\cos ^2 A+2 \sin B \cos A$ $=a^2+b^2$ $\begin{aligned} & \Rightarrow \quad 2 \sin (A+B)+2=a^2+b^2 \\ & \Rightarrow \quad \sin (A+B)=\frac{a^2+b^2-2}{2}\end{aligned}$

Hence, the correct answer is option: 'C'.

If $\sin A+\cos B=a$ and $\sin B+\cos A=b$, then $\sin (A+B)$ is equal to

Solution

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