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$text If end text cos space A equals 5 over 13 comma tan space B equals fraction numerator negative 15 over denominator 8 end fraction comma negative 270 to the power of ring operator less than straight A less than 360 to the power of ring operator comma 90 to the power of ring operator less than straight B less than 180 to the power of ring operator$ , then the quadrant to which A+B belongs is

IV
III
II
I

The correct answer is: II

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In a $triangle A B C comma fraction numerator t a n invisible function application B over denominator t a n invisible function application C end fraction equals 2 over 3$ and $t a n invisible function application A t a n invisible function application B t a n invisible function application C equals 6$ then the value(s) satisfy the equation

In a $triangle A B C comma fraction numerator t a n invisible function application B over denominator t a n invisible function application C end fraction equals 2 over 3$ and $t a n invisible function application A t a n invisible function application B t a n invisible function application C equals 6$ then the value(s) satisfy the equation

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$t a n space 40 to the power of ring operator plus t a n space 80 to the power of ring operator minus √ 3 t a n space 40 to the power of ring operator t a n space 80 to the power of ring operator equals$

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$text If end text 0 less than theta less than pi over 2 text and end text 2 sin invisible function application theta equals square root of 3 cos space 10 to the power of ring operator plus sin space 10 to the power of ring operator text then end text theta equals$

parallel

$cos space left parenthesis n plus 1 right parenthesis alpha cos space left parenthesis n minus 1 right parenthesis alpha plus sin space left parenthesis n plus 1 right parenthesis alpha sin space left parenthesis n minus 1 right parenthesis alpha equals$

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Assertion A: In a right-angled triangle $s i n squared space A plus s i n squared space B plus s e c squared space C equals 2$ Reason $R colon$ if $alpha comma beta$ are complementary angles then $s i n squared space alpha plus s i n squared space beta equals 1$

parallel

AB is a line segment of length 24 cm and C is its middle point. On AB, A and CB semi-circles are described. The radius of circle which touches all these semi-circles is

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in a $triangle P Q R$ $3 sin space P plus 4 cos space Q equals 6$ and $4 sin space Q plus 3 cos$ p=1 then

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if $straight f subscript straight k left parenthesis straight x right parenthesis equals 1 divided by straight k left parenthesis sin to the power of straight k space straight x plus cos to the power of straight k space straight x right parenthesis$ where $straight x element of straight R comma straight k greater or equal than 1$ then $straight f subscript 4 left parenthesis straight x right parenthesis minus straight f subscript 6 left parenthesis straight x right parenthesis equals$

if $straight f subscript straight k left parenthesis straight x right parenthesis equals 1 divided by straight k left parenthesis sin to the power of straight k space straight x plus cos to the power of straight k space straight x right parenthesis$ where $straight x element of straight R comma straight k greater or equal than 1$ then $straight f subscript 4 left parenthesis straight x right parenthesis minus straight f subscript 6 left parenthesis straight x right parenthesis equals$

Two arcs of same length of two different circles subtended angles of $25 to the power of ring operator$ and $75 to the power of ring operator$ at their centers respectively. Then the ratio of the radii of the circles is

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$straight a equals sec space 2 to the power of ring operator comma straight b equals sec space 2 rightwards double arrow$

$straight a equals sec space 2 to the power of ring operator comma straight b equals sec space 2 rightwards double arrow$

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If ABCD is a cynic quadrilateral such that 12 tan $A minus 5 equals 0$ and 5cos B+3=0, then cos C tan D=

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