If sin α + cos α = p , then what is cos 2 ( 2 α ) equal to?

Question

If sin α + cos α = p , then what is cos 2 ( 2 α ) equal to?, P 2, p 2 − 1, P 2 ( 2 − p 2 ), p 2 + 1

MARKS App · Accepted Answer

\sin \alpha+\cos \alpha=p \ & \Rightarrow(\sin \alpha+\cos \alpha)^{2}=p^{2} \ & \Rightarrow \sin ^{2} \alpha+\cos ^{2} \alpha+2 \sin \alpha \cos \alpha=p^{2} \ & \Rightarrow 1+\sin 2 \alpha=p^{2} \ & \Rightarrow \sin 2 \alpha=\mathrm{p}^{2}-1 \ & \cos ^{2} 2 \alpha=1-\sin ^{2} 2 \alpha=1-\left(\mathrm{p}^{2}-1ight)^{2} \ &=1-\left(\mathrm{p}^{4}+1-2 \mathrm{p}^{2}ight)=-\mathrm{p}^{4}+2 \mathrm{p}^{2} \ &=\mathrm{p}^{2}\left(2-\mathrm{p}^{2}ight) \

Search any question & find its solution

Looking for more such questions to practice?