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

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

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

simplify

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

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

Solution steps

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

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}

sin (x - \frac{5 π}{3})

cos (2 x + 3 0^{\circ})

cos (arctan (x \frac{1}{3}))

2 + sin (x - \frac{π}{2})

3 sin (8 x + \frac{π}{2})

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