If \(\sin\theta=\frac7{25}\), find \(\cos^2\theta\).
\(\frac{576}{625}\)
\(\frac{718}{525}\)
\(\frac{756}{325}\)
\(\frac{347}{125}\)
Answer: A
Using the identity:
\[
\sin^2\theta+\cos^2\theta=1
\]
Therefore,
\[
\cos^2\theta=1-\sin^2\theta
\]
Substituting:
\[
\cos^2\theta=1-\left(\frac7{25}\right)^2
\]
\[
=1-\frac{49}{625}
\]
\[
=\frac{625-49}{625}
\]
\[
\boxed{\frac{576}{625}}
\]
Trick Explanation/Solution: When \(\sin\theta\) is given and \(\cos^2\theta\) is required, use \(\cos^2\theta=1-\sin^2\theta\) directly.
यदि \(\sin\theta=\frac7{25}\), तो ज्ञात कीजिए \(\cos^2\theta\)।
\(\frac{576}{625}\)
\(\frac{718}{525}\)
\(\frac{756}{325}\)
\(\frac{347}{125}\)
उत्तर: A
Using the identity:
\[
\sin^2\theta+\cos^2\theta=1
\]
Therefore,
\[
\cos^2\theta=1-\sin^2\theta
\]
Substituting:
\[
\cos^2\theta=1-\left(\frac7{25}\right)^2
\]
\[
=1-\frac{49}{625}
\]
\[
=\frac{625-49}{625}
\]
\[
\boxed{\frac{576}{625}}
\]
Trick Explanation/Solution: When \(\sin\theta\) is given and \(\cos^2\theta\) is required, use \(\cos^2\theta=1-\sin^2\theta\) directly.
Community answers
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- Option C\(\frac{756}{325}\)
I think C correct because 245/459-2 2.4244
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