Question:
If \(\sin A = \dfrac{5}{13}\), what is \(\cos A\)?
यदि \(\sin A = \dfrac{5}{13}\) है, तो \(\cos A\) का मान क्या होगा?
Options:
- \(\dfrac{12}{13}\)
- \(\dfrac{13}{14}\)
- \(\dfrac{5}{12}\)
- \(\dfrac{7}{13}\)
- \(\dfrac{12}{13}\)
- \(\dfrac{13}{14}\)
- \(\dfrac{5}{12}\)
- \(\dfrac{7}{13}\)
Correct Answer: a)
Explanation:
Using \(\cos A = \sqrt{1 – \sin^2 A} = \sqrt{1 – \left(\dfrac{5}{13}\right)^2} = \sqrt{1 – \dfrac{25}{169}} = \sqrt{\dfrac{144}{169}} = \dfrac{12}{13}\).
\(\cos A = \sqrt{1 – \sin^2 A} = \sqrt{1 – \dfrac{25}{169}} = \sqrt{\dfrac{144}{169}} = \dfrac{12}{13}\)। विकल्प (a) सही है।