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Mathematics : Introduction to Trigonometry

Short Answer Type

171. Find the value of x in the following:
If sin 2.x = sin 60° . cos 30° - cos 60° . sin 30°

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172. Find the value of x in the following:
If cos (40° + x) = sin 30°.

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173. Determine x, if

fraction numerator straight x space sin squared 30 degree. space cos squared space 60 degree over denominator 4 space cos to the power of 2 space end exponent 45 degree end fraction space equals space fraction numerator 3 space sin squared 45 degree plus 2 cos squared 30 degree over denominator sin squared 90 degree minus 4 cos squared 45 degree end fraction.

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Long Answer Type

174.

If $sin left parenthesis straight A plus straight B plus straight C right parenthesis equals space 1 comma space space tan space left parenthesis straight A minus straight B right parenthesis space equals space fraction numerator 1 over denominator square root of 3 end fraction space and space sec left parenthesis straight A plus straight C right parenthesis space equals 2 comma$ find A, B and C when they are acute.

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175.

If $sin left parenthesis straight A plus 2 straight B right parenthesis space equals space fraction numerator square root of 3 over denominator 2 end fraction space and space cos space left parenthesis straight A plus 4 straight B right parenthesis$ . Find A and B.