(A) If tan θ=24/7, then find the value of sin θ+ cos θ.

\[\begin{aligned} & \tan \theta=\frac{24}{7}=\frac{P}{B} \\ & \text { Getting, } \sin \theta=\frac{24}{25} \text { and } \cos \theta=\frac{7}{25} \\ & \begin{aligned} \therefore \sin \theta+\cos \theta & =\frac{24}{25}+\frac{7}{25} \\ & =\frac{31}{25} \end{aligned} \end{aligned} \]

\[\begin{aligned} \frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)} & =\frac{1-\sin ^{2} \theta}{1-\cos ^{2} \theta} \\ & =\frac{\cos ^{2} \theta}{\sin ^{2} \theta}=\cot ^{2} \theta \\ & =\left(\frac{7}{8}\right)^{2}=\frac{49}{64} \end{aligned} \]