Question

what is another expression for cos x-sin x

Answer 1

options
A \[\sqrt{2} \cos \left( x+\frac{ \pi }{ 4 } \right)\]

Answer 2

\[\sqrt{2}\cos \left( x-\frac{ \pi }{ 4} \right)\]

Answer 3

C
\[2\cos \left( x+\frac{ \pi }{ 4} \right)\]

Answer 4

D
\[2\cos \left( x-\frac{ \pi}{ 4 } \right)\]

Answer 5

please help!!!

Answer 6

@ganeshie8

Answer 7

hint:
if I multiply and divide the left side by sqrt(2), I get this:
\[\Large \sqrt 2 \left( {\frac{1}{{\sqrt 2 }}\cos x - \frac{1}{{\sqrt 2 }}\sin x} \right)\]

Answer 8

now, please keep in mind that:
\[\Large \frac{1}{{\sqrt 2 }} = \cos \left( {\frac{\pi }{4}} \right) = \sin \left( {\frac{\pi }{4}} \right)\]

Answer 9

hint:
\[\Large \begin{gathered}
\cos x - \sin x = \sqrt 2 \left( {\frac{1}{{\sqrt 2 }}\cos x - \frac{1}{{\sqrt 2 }}\sin x} \right) \hfill \\
\hfill \\
= \sqrt 2 \left( {\cos \left( {\frac{\pi }{4}} \right)\cos x - \sin \left( {\frac{\pi }{4}} \right)\sin x} \right) \hfill \\
\end{gathered} \]

Answer 10

ok,, 10nks.. but still stuck on how to simplify further

Answer 11

we can apply this identity:
\[\Large \cos \left( {\alpha + \beta } \right) = \cos \alpha \cos \beta - \sin \alpha \sin \beta \]

Answer 12

ok so that'll be \[\sqrt{2}(\cos(x+\frac{ \pi }{ 4}))\]

Answer 13

that's right!

Answer 14

so the correct answer will be A

Answer 15

yes! it is option A)

Answer 16

oh ok,, thank u very much..

Answer 17

:)