Question : If $\sin A+\sin ^2 A=1$, then the value of $\cos ^4 A+\cos ^6 A$ is:
Option 1: $\cos A$
Option 2: $\sin A$
Option 3: 1
Option 4: 0
Correct Answer: $\sin A$
Solution :
Given: $\sin A+\sin ^2 A=1$
⇒ $\sin A=1-\sin ^2 A$
⇒ $\sin A=\cos ^2 A$
⇒ $\sin^2 A=\cos ^4 A$
Now,
$\cos ^4 A+\cos ^6 A$
= $\cos^2 A(\cos ^2 A+\cos ^4 A)$
Putting the values, we get:
= $\sin A(\sin A+\sin^2 A)$
Since, $\sin A+\sin ^2 A=1$
= $\sin A\times 1$
= $\sin A$
Hence, the correct answer is $\sin A$.
Related Questions
Question : If $\cos A + \cos B + \cos C = 3$, then what is the value of $\sin A + \sin B + \sin C$?
Question : If $\cos \theta+\sec \theta=2$, then the value of $\sin ^6 \theta+\cos ^6 \theta$ is:
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