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Trigonometric Functions

Short Answer Type

411.

Solve the following equation:

$4 space cos squared straight x plus 6 space sin squared straight x equals 5$

116 Views

412.
Solve the following equation:

$space 2 space sin squared straight x space plus space sin squared 2 straight x space equals space 2$

Solution not provided.

Ans. $straight x equals left parenthesis 2 straight n plus 1 right parenthesis straight pi over 2 space space or space space straight x equals nπ plus-or-minus straight pi over 4 comma space straight n space element of space straight Z$

106 Views

413.

Solve the following equation:

$space space space space 3 space cos squared straight x minus 2 square root of 3 space sinx space cosx space minus space 3 sin squared straight x space equals space 0$

110 Views

414.

In $increment ABC comma space straight a equals 18 comma space straight b equals 24 comma space straight c equals 30 comma$ find the value of

cos A and cos C

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415.

In $increment ABC comma space straight a equals 18 comma space straight b equals 24 comma space straight c equals 30 comma$ find the value of

$tan straight B over 2 space and space tan straight C over 2$

100 Views

416.

In $increment ABC comma space straight a equals 18 comma space straight b equals 24 comma space straight c equals 30 comma$ find the value of

$sin space straight A space and space sin space straight B$

118 Views

417.

In triangle ABC, show that

$fraction numerator straight a plus straight b over denominator straight c end fraction equals fraction numerator cos open parentheses begin display style fraction numerator straight A minus straight B over denominator 2 end fraction end style close parentheses over denominator sin open parentheses begin display style straight C over 2 end style close parentheses end fraction$

105 Views

418.

In triangle ABC, show that

$fraction numerator straight b squared minus straight c squared over denominator straight a squared end fraction equals fraction numerator sin space left parenthesis straight B minus straight C right parenthesis over denominator sin space left parenthesis straight B plus straight C right parenthesis end fraction$

114 Views

419.

In triangle ABC, show that

$space space straight a space left parenthesis sinB space minus space sin space straight C right parenthesis space plus space straight b space left parenthesis sin space straight C space minus space sin space straight A right parenthesis space plus space straight c space left parenthesis sin space straight A space minus space sin space straight B right parenthesis space equals 0$

111 Views

420.

In triangle ABC, show that

$fraction numerator straight c minus straight a over denominator straight b end fraction cos open parentheses straight B over 2 close parentheses equals sin open parentheses fraction numerator straight C minus straight A over denominator 2 end fraction close parentheses$