What is 2cos(x)+7cos(x-45) ?

The solution to 2cos(x)+7cos(x-45) is 2cos(x)+(7(sqrt(2)cos(x)+sqrt(2)sin(x)))/2

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simplify 2cos(x)+7cos(x-45)

simplify

2 cos (x) + 7 cos (x - 4 5^{\circ})

2 cos (x) + \frac{7 ( 2 cos ( x ) + 2 sin ( x ) )}{2}

Solution steps

2 cos (x) + 7 cos (x - 4 5^{\circ})

Rewrite using trig identities

= 2 cos (x) + 7 \cdot \frac{2 cos ( x ) + 2 sin ( x )}{2}

Multiply

7 \cdot \frac{2 cos ( x ) + 2 sin ( x )}{2} : \frac{7 ( 2 cos ( x ) + 2 sin ( x ) )}{2}

= 2 cos (x) + \frac{7 ( 2 cos ( x ) + 2 sin ( x ) )}{2}

Simplify

2 cos (x) + 2 sin (x) : 2 sin (x + \frac{π}{4})

= 2 cos (x) + \frac{7 \cdot 2 sin ( x + \frac{π}{4} )}{2}

\frac{7 \cdot 2 sin ( \frac{π}{4} + x )}{2} = \frac{7 ( 2 cos ( x ) + 2 sin ( x ) )}{2}

= 2 cos (x) + \frac{7 ( 2 cos ( x ) + 2 sin ( x ) )}{2}

\frac{1 - sin ^{2} ( x )}{d x}

\frac{1}{sec ( v )} d v

10 sin (x + 6 0^{\circ})

2 cos^{x} (+ cos (x) - 1 (0.2 π))

- cos (\frac{π}{4} + t)

What is 2cos(x)+7cos(x-45) ?
The solution to 2cos(x)+7cos(x-45) is 2cos(x)+(7(sqrt(2)cos(x)+sqrt(2)sin(x)))/2