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Schach [20]
3 years ago
13

Can someone help me ? i have no clue how to figure this out

Mathematics
2 answers:
Crank3 years ago
7 0

\cos \: t ( \sec \: t -  \cos \: t) =  \sin^{2}t \\  \\ 1. \: 1 -  \frac{ \cos \: t }{ \sec \: t }   =  \sin^{2} t \\ 2. \: 1 -  \cos \: t   \cos \: t =  \sin^{2} t \\ 3. \: 1 -  \cos^{2} t =  \sin^{2} t \\ 4. \: 1 -  \cos^{2} t -  \sin^{2} t = 0 \\ 5. \: 1 - 1 = 0 \\ 6. \: 0 = 0 \\ 7. \: infinitely \: many \: solutions

Ad libitum [116K]3 years ago
5 0

\cos t (\sec t - \cos t) = \sin^2 t

\cos t (\dfrac{1}{\cos t} - \cos t) = \sin^2 t

\dfrac{\cos t}{\cos t} - \cos^2 t = \sin^2 t

1 - \cos^2 t = \sin^2 t

Use the identity: \sin^2 t + \cos^2 t = 1 and solve for \sin^2 t. You get: \sin^2 t = 1 - \cos^2 t

Do the substitution on the left side to get:

\sin^2 t = \sin ^2 t

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