TS EAMCET · Maths · Trigonometric Ratios & Identities
\(\sin \alpha+\cos \alpha=m \Rightarrow \sin ^6 \alpha+\cos ^6 \alpha=\)
- A \(\frac{4+3\left(m^2-1\right)^2}{4}\)
- B \(\frac{4-3\left(m^2-1\right)^2}{4}\)
- C \(\frac{3+4\left(m^2-1\right)^2}{4}\)
- D \(\frac{4-3\left(m^2+1\right)^2}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{4-3\left(m^2-1\right)^2}{4}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \sin \alpha+\cos \alpha=m \\ & \sin ^6 \alpha+\cos ^6 \alpha=\left(\sin ^2 \alpha\right)^3+\left(\cos ^2 \alpha\right)^3 \\ & =\left(\sin ^2 \alpha+\cos ^2 \alpha\right)\left(\sin ^4 \alpha-\sin ^2 \alpha \cos ^2 \alpha+\cos ^4 \alpha\right) \\ &…
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