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Trigonometric Functions

Short Answer Type

241.

Find the value of:

$cot left parenthesis negative 315 degree right parenthesis$

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242.

Find the value of:

$sec open parentheses fraction numerator 11 straight pi over denominator 4 end fraction close parentheses$

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243.

Find the value of:

$sin left parenthesis negative 765 degree right parenthesis$

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244.

Find the value of:

$cosec left parenthesis negative 1770 degree right parenthesis$

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245.

Simplify the following:

$space space space sin left parenthesis 90 degree plus straight theta right parenthesis space tan left parenthesis 270 degree plus straight theta right parenthesis space cot left parenthesis 90 degree plus straight theta right parenthesis space cosec left parenthesis 270 degree plus straight theta right parenthesis$

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246.

Simplify the following:

$fraction numerator cos left parenthesis 2 straight pi minus straight theta right parenthesis space cos left parenthesis straight pi plus straight theta right parenthesis space cot open parentheses begin display style straight pi over 2 end style minus straight theta close parentheses over denominator sin open parentheses begin display style straight pi over 2 end style plus straight theta close parentheses space cos left parenthesis negative straight theta right parenthesis end fraction$

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247.
In any triangle ABC, prove that:

$tan open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses space equals space cot open parentheses straight C over 2 close parentheses$

Solution not provided.

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248.

In any triangle ABC, prove that:

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249.

If $space space 80 space equals space straight pi comma$ prove that $cosθ space plus space cos space 7 straight theta space equals space 0.$

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250.

If $space space straight B plus straight C space equals space straight pi over 3 comma$ show that $sin open parentheses fraction numerator 2 straight pi over denominator 3 end fraction minus straight B close parentheses space equals space sin open parentheses fraction numerator 2 straight pi over denominator 3 end fraction minus straight C close parentheses$