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Basic Inverse Trigonometric Functions

The absolute ...

Question

The absolute value of the expression $tan \frac{π}{16} + tan \frac{5 π}{16} + tan \frac{9 π}{16} + tan \frac{13 π}{16}$ is

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Solution

$tan \frac{π}{16} + tan \frac{5 π}{16} + tan \frac{9 π}{16} + tan \frac{13 π}{16} ⟹ \frac{sin \frac{π}{16}}{cos \frac{π}{16}} + \frac{sin \frac{9 π}{16}}{cos \frac{9 π}{16}} + \frac{sin \frac{5 π}{16}}{cos \frac{5 π}{16}} + \frac{sin \frac{13 π}{16}}{c o s \frac{13 π}{16}}$

$w e k n o w t h a t s i n (A + B) = s i n A c o s B + c o s A s i n B A n d 2 c o s A c o s B = c o s (A + B) + c o s (A - B)$

$S o w e g e t ⟹ \frac{s i n \frac{π}{16} c o s \frac{9 π}{16} + s i n \frac{9 π}{16} c o s \frac{π}{16}}{c o s \frac{π}{16} c o s \frac{9 π}{16}} + \frac{s i n \frac{5 π}{16} c o s \frac{13 π}{16} + s i n \frac{13 π}{16} c o s \frac{5 π}{16}}{c o s \frac{5 π}{16} c o s \frac{13 π}{16}} ⟹ \frac{2 s i n \frac{10 π}{16}}{c o s \frac{10 π}{16} + c o s \frac{π}{2}} + \frac{2 s i n \frac{18 π}{16}}{c o s \frac{18 π}{16} + c o s \frac{π}{2}} ⟹ \frac{2 s i n \frac{5 π}{8}}{c o s \frac{5 π}{8}} + \frac{2 s i n \frac{9 π}{8}}{c o s \frac{9 π}{8}} ⟹ \frac{2 s i n \frac{14 π}{8}}{c o s \frac{5 π}{8} c o s \frac{9 π}{8}} ⟹ \frac{4 s i n \frac{7 π}{4}}{c o s \frac{7 π}{4} + c o s \frac{π}{2}} ⟹ 4 t a n \frac{7 π}{4} = - 4 S o t h e a b s o l u t e v a l u e i s 4$

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Similar questions

Q. The absolute value of

tan \frac{π}{16} + tan \frac{5 π}{16} + tan \frac{9 π}{16} + tan \frac{13 π}{16}

Q. The absolute value of

tan \frac{π}{16} + tan \frac{5 π}{16} + tan \frac{9 π}{16} + tan \frac{13 π}{16}

Q. The value of the equation

tan (\frac{π}{12}) \cdot tan (\frac{π}{16}) \cdot tan (\frac{5 π}{12}) \cdot tan (\frac{7 π}{16})

tan \frac{π}{16} + tan \frac{3 π}{16} + tan \frac{5 π}{16} + tan \frac{7 π}{16}

Q. The value of

t a n \frac{π}{16}

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