Question : If $\sin A=\frac{3}{5}$, calculate the value of $\cos A+\tan A-1$.
Option 1: $\frac{21}{20}$
Option 2: $\frac{11}{20}$
Option 3: $\frac{13}{20}$
Option 4: $2$
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Correct Answer: $\frac{11}{20}$
Solution : $\sin A=\frac{3}{5}$ $⇒\cos A = \sqrt{1-\sin^2A}$ $⇒\cos A = \sqrt{1-(\frac{3}{5})^2}$ $⇒\cos A = \sqrt{\frac{25-9}{25}}$ $⇒\cos A = \sqrt{\frac{16}{25}}$ $⇒\cos A = \frac{4}{5}$ We know, $\tan A = \frac{\sin A}{\cos A}$ $⇒\tan A = \frac{\frac{3}{5}}{\frac{4}{5}}$ $⇒\tan A = \frac{3}{4}$ So, $\cos A+\tan A-1 = \frac{4}{5} + \frac{3}{4} -1 = \frac{16+15-20}{20}= \frac{11}{20}$ Hence, the correct answer is $\frac{11}{20}$.
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