Question

solve it.
$cos(a + 45) = 1 \div \sqrt{2}(c \\ os \: a - sin \: a)$
solve it. ​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\sf{cos(\alpha+45^{\circ})$

Using the formula,

$\bullet\,\tt{\green{\large{cos(A+B)=cos(A)cos(B)-sin(A)sin(B)}}}$

so,

$\sf{cos(\alpha+45^{\circ})=cos(\alpha)cos(45^{\circ})-sin(\alpha)sin(45^{\circ})}$

$\sf{\implies\,cos(\alpha+45^{\circ})=cos(\alpha)\cdot\dfrac{1}{\sqrt{2}}-sin(\alpha)\cdot\dfrac{1}{\sqrt{2}}}$

$\sf{\implies\,cos(\alpha+45^{\circ})=\dfrac{1}{\sqrt{2}}\{cos(\alpha)-sin(\alpha)\}}$