Sin(30-x)+cos(60-x)=cosx

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Solution for Sin(30-x)+cos(60-x)=cosx equation: 


Simplifying
Sin(30 + -1x) + cos(60 + -1x) = cosx
(30 * inS + -1x * inS) + cos(60 + -1x) = cosx
(30inS + -1inxS) + cos(60 + -1x) = cosx
30inS + -1inxS + (60 * cos + -1x * cos) = cosx
30inS + -1inxS + (60cos + -1cosx) = cosx

Reorder the terms:
60cos + -1cosx + 30inS + -1inxS = cosx

Solving
60cos + -1cosx + 30inS + -1inxS = cosx

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-1cosx' to each side of the equation.
60cos + -1cosx + 30inS + -1cosx + -1inxS = cosx + -1cosx

Reorder the terms:
60cos + -1cosx + -1cosx + 30inS + -1inxS = cosx + -1cosx

Combine like terms: -1cosx + -1cosx = -2cosx
60cos + -2cosx + 30inS + -1inxS = cosx + -1cosx

Combine like terms: cosx + -1cosx = 0
60cos + -2cosx + 30inS + -1inxS = 0

Add '-30inS' to each side of the equation.
60cos + -2cosx + 30inS + -30inS + -1inxS = 0 + -30inS

Combine like terms: 30inS + -30inS = 0
60cos + -2cosx + 0 + -1inxS = 0 + -30inS
60cos + -2cosx + -1inxS = 0 + -30inS
Remove the zero:
60cos + -2cosx + -1inxS = -30inS

Add 'inxS' to each side of the equation.
60cos + -2cosx + -1inxS + inxS = -30inS + inxS

Combine like terms: -1inxS + inxS = 0
60cos + -2cosx + 0 = -30inS + inxS
60cos + -2cosx = -30inS + inxS

Reorder the terms:
60cos + -2cosx + 30inS + -1inxS = -30inS + 30inS + inxS + -1inxS

Combine like terms: -30inS + 30inS = 0
60cos + -2cosx + 30inS + -1inxS = 0 + inxS + -1inxS
60cos + -2cosx + 30inS + -1inxS = inxS + -1inxS

Combine like terms: inxS + -1inxS = 0
60cos + -2cosx + 30inS + -1inxS = 0

The solution to this equation could not be determined.

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