Question

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Answer 1

The solution of the given trigonometric equation

`x = (\pi )/(6)`

Explanation:

Step(i):-

Given

`cos( 3x - (\pi )/(3) ) = (√(3) )/(2)`

`cos( 3x - (\pi )/(3) ) = cos ((\pi )/(6) )`

`3x - (\pi )/(3) = (\pi )/(6)`

`3x - (\pi )/(3 ) + (\pi )/(3) = (\pi )/(6) + (\pi )/(3)`

`3x = (2\pi +\pi )/(6) = (3\pi )/(6) = (\pi )/(2)`

`x = (\pi )/(6)`

Step(ii):-

The solution of the given trigonometric equation

`x = (\pi )/(6)`

verification :-

`cos( 3x - (\pi )/(3) ) = (√(3) )/(2)`

put
`x = (\pi )/(6)`

`cos( 3((\pi )/(6)) - (\pi )/(3) ) = (√(3) )/(2)`

`cos ((\pi )/(6) ) = (√(3) )/(2) \\\\(√(3) )/(2) = (√(3) )/(2)`

Both are equal

∴The solution of the given trigonometric equation

`x = (\pi )/(6)`