Question

Assertion (A): lf $\frac{5x+1}{(x+2)(x-1)}=\frac{A}{(x+2)}+\frac{B}{(x-1)}$ and $\sin \theta =(A+B)$ then $\sin \theta$ does not exist

Reason (R) : $\sin \theta \in [-1,1]$

• A. Both A and R are true and R is correct explanation of A
• B. Both A and R are true and R is not correct explanation of A
• C. A is true and R is false
• D. A is false and R is true

Answer 1

The correct option is A Both A and R are true and R is correct explanation of A

Given, $\frac{5x+1}{(x+2)(x-1)}=\frac{A}{(x+2)}+\frac{B}{(x-1)}$
$\Rightarrow 5x+1=A(x-1)+B(x+2)$
$A+B=5,-A+2B=1$
Also, given $\sin \theta =A+B$
$\Rightarrow \sin \theta =5$
which is not possible because $\sin \theta \in [-1,1]$
Hence, A+B does not exists .
Hence, assertion and reason are correct. Reason is correct explanation of reason.