KCET · Maths · Trigonometric Ratios & Identities
If \(\cos x+\cos ^2 x=1\), then the value of \(\sin ^2 x+\sin ^4 x\) is
- A \(-1\)
- B \(1\)
- C \(0\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \cos x+\cos ^2 x=1 \\ & \Rightarrow 1-\cos ^2 x=\cos x \quad \Rightarrow \sin ^2 x=\cos x \\ & \Rightarrow \sin ^2 x+\sin ^4 x \\ & \Rightarrow \cos x+(\cos x)^2=1\end{aligned}\)
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