Question

A value of theta satisfying cos theta + root 3 sin theta = 2 is

Answer 1

Answer:

Ф =  2 n π + π / 6 .

Explanation:

Given  :

cos Ф + √ 3 sin Ф  = 2

Diving by 2

1 /  2 cos Ф  + √ 3 / 2 sin Ф  = 2 / 2

We know 1 / 2 is equal to cos π / 3 and √ 3 / 2 = sin π / 3

1 /  2 cos Ф  + √ 3 / 2 sin Ф  = 1

cos  π / 3 . cos Ф + sin  π / 3 . sin Ф = 1

using cos ( A - B ) = cos A cos B + sin A sin B

cos ( Ф + π / 3 ) = cos 0     [ Replaced 1 as cos 0 ]

cos 0 = 2 n π + π / 2

Ф + π / 3  = 2 n π + π / 2

Ф =  2 n π + π / 2 -  π / 3

Ф =  2 n π + π / 6 .

Hence the value of theta is 2 n π + π / 6 .  .

Answer 2

Answer:

$question \:$

$a \: value \: of \: theta \: + root \: 3sin \: theta \: = 2 \: is$

$solution$

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