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Mathematics : Trigonometric Functions

Short Answer Type

371.

If $cosx space equals space 1 half open parentheses straight p plus 1 over straight p close parentheses comma$ show that:

$2 space cos space 4 straight theta space equals space open parentheses straight p to the power of 4 plus 1 over straight p to the power of 4 close parentheses$

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372.

Prove that: $space space space space space space fraction numerator sin space 5 straight x minus 2 sin space 3 straight x space plus space sin space straight x over denominator cos space 5 straight x space minus space cos space straight x end fraction equals space tan space straight x$

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373.

Show that: $sin squared straight A plus sin squared space left parenthesis straight A minus straight B right parenthesis minus 2 space sinA space cosB space sin left parenthesis straight A minus straight B right parenthesis equals sin squared straight B$

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374.

Show that:

$4 space sin space straight A space sin space straight B space sin space straight C space equals space sin space left parenthesis straight B plus straight C minus straight A right parenthesis plus sin space left parenthesis straight C plus straight A minus straight B right parenthesis plus sin space left parenthesis straight A plus straight B minus straight C right parenthesis minus sin space left parenthesis straight A plus straight B plus straight C right parenthesis$

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375.

Prove that:

$space space space cos squared straight x plus cos squared open parentheses straight x plus straight pi over 3 close parentheses plus cos squared open parentheses straight x minus straight pi over 3 close parentheses equals 3 over 2$

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376.

Find the principal solutions of the equation:

$tanx space equals space minus fraction numerator 1 over denominator square root of 3 end fraction$

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377.

Find the principal solutions of the equation:

$sinx space equals space minus 1 half$

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378.

Find the principal solutions of the equation:

$cosx equals fraction numerator negative square root of 3 over denominator 2 end fraction$

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379.

Find the principal solutions of the equation:

$secx space equals space square root of 2$

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380.

Find the principal solutions of the equation:

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