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Question

Mathematics Question on Trigonometric Identities

If tanθ=−43,tan \theta=-\frac{4}{3}, then sinθsin \theta is

A

−45butnot45-\frac{4}{5} but not \frac{4}{5}

B

−45or45-\frac{4}{5} or \frac{4}{5}

C

−45butnot−45-\frac{4}{5} but not -\frac{4}{5}

D

None of the above

Answer

−45or45-\frac{4}{5} or \frac{4}{5}

Explanation

Solution

Since, tanθ<0.tan \theta < 0.
∴Angleθ is either in the second or fourth quadrant.\therefore Angle \theta \text{ is either in the second or fourth quadrant.}
Then, \hspace15mm sin \theta > 0 or < 0
∴sinθmaybe45or−45\therefore sin \theta may be \frac{4}{5} or -\frac{4}{5}