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Trigonometric Functions

Short Answer Type

481.

Simplify:

$space space fraction numerator cos left parenthesis 2 straight pi plus straight theta right parenthesis space cosec left parenthesis 2 straight pi plus straight theta right parenthesis space tan open parentheses begin display style straight pi over 2 plus straight theta end style close parentheses over denominator sec open parentheses begin display style straight pi over 2 plus straight theta end style close parentheses space cosθ space cot left parenthesis straight pi plus straight theta right parenthesis end fraction$

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482.

Prove that: $open curly brackets 1 plus cotx minus sec open parentheses straight pi over 2 plus straight x close parentheses close curly brackets space open curly brackets 1 plus cotx plus sec open parentheses straight pi over 2 plus straight x close parentheses close curly brackets space equals space 2 cotx$

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Long Answer Type

483.

In a cyclic quadrilateral ABCD, show that (a) sin A = sin C (b) cos B + cos D = 0.

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Short Answer Type

484.

Show that:

$space space cos squared straight x plus cos squared left parenthesis straight x plus 120 degree right parenthesis plus cos squared left parenthesis straight x minus 120 degree right parenthesis space equals space 3 over 2$

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485.

If 2 tanx = 3 tany, show that tan(x - y) = $fraction numerator sin space 2 straight y over denominator 5 space minus space cos 2 straight y end fraction.$

168 Views

486.

Show that: $cosA. space cos 2 straight A. space cos 2 squared straight A. space cos 2 cubed straight A. space......... cos space 2 to the power of straight n minus 1 end exponent space straight A space equals space fraction numerator sin space 2 to the power of straight n straight A over denominator 2 to the power of straight n sinA end fraction$

103 Views

487.

If $straight n space tan open parentheses straight x over 2 close parentheses space equals space straight m comma space prove space that space straight m space sinx space plus space straight n space cosx space equals space straight n$