Question

Find the value of tan (-690)​

Answer 1

Remmember :-

$\bold{\large{\: \implies \: tan \: ( - theta)}} = \bold{ \large{ - tan \: (theta)}} \\ \\ \: \bold{ \large{ \implies \: tan \: (360 \times n - theta) = - \: tan \: (theta)}}$

Solution :-

$\bold{ \large{ \implies \: \ \: tan \: ( \: - 690 \: ) }} \\ \\ \implies \: \: \: \: \: \bold{ \large{ - tan \: ( \: 690 \: )}} \\ \\ \bold{ \large{\implies \: \: \: - tan \: ( \: 360 \times 2 - 30 \: )}} \\ \\ \bold{ \large{ \implies \: \: \: - ( - tan \: 30 \: )}} \\ \\ \bold{ \large{ \implies \: \: \: \: tan \: 30}} \\ \\ \bold{ \large{ \implies \: \: \: \: \: \: \frac{1}{ \sqrt{3} } }}$

Answer 2

$\large{ \bold{ \fbox{ \fbox{ \: \: Given \: :- }}}}$

$\to \bold{Tan \: ( - \: 690 ) \: }$

$\large \bold{ \fbox{ \fbox{ \: \: To \: Find \: :- }}}$

$\to \bold{Value \: Of \:Tan \: ( - \: 690 ) \: \: }$

$\large \bold{\fbox{ \fbox{ \: \: Solution \: :- }}}$

$\to\bold{Tan ( - \: 690 ) \: } \\ \\ \to\bold{- Tan ( 360 × 2 - 30)\: } \\ \\ \to \bold{- ( - Tan \: 30 ) \: } \\ \\ \to \bold{ \: \: \: \: \: \: \: \frac{1}{ \sqrt{3} } }$

$\large\fbox{ \fbox{ \bold{ \: \: Identity \: Used \: :- }}}$

$\to \: \bold{Tan \: ( - \: Φ ) = - \: Tan \: Φ \: } \\ \to \: \bold{Tan \: ( 360 × n - \: Φ ) = - \: Tan \: Φ \: }$