Question

If sinx=4/5 and x is in quadrant 2, then tan2x= -12/7 24/7 -24/7 12/7

Answer 1

24/7 .........................................................................................

Answer 2

Answer:

Hence, the value of tan2x is:

                            24/7

Step-by-step explanation:

We are given sine trignometric ratio as:

$\sin x=\dfrac{4}{5}$

Aklso the angle ''x'' lie in the second quadrant.

As we know that the trignometric ratios which are positive in second quadrant are:

Sine(sin) and cosecant(csc)

whereas the other trignometric ratio's i.e. cosine(cos),secant(sec),cotangent(cot),tangent(tan) are all negative in second quadrant.

We know that the sine trignometric function is the ratio of perpendicular to hypotenuse of a right angled triangle corresponding to angle 'x'.

i.e. Let P=4 and H=5

As we know that in a right triangle we have:

$H^2=P^2+B^2\\\\5^2=4^2+B^2\\\\25=16+B^2\\\\B^2=25-16\\\\B^2=9\\\\B=3$

Also as we know,

$\tan x=\dfrac{P}{B}\\\\i.e.\\\\\tan x=-\dfrac{4}{3}$

(The value is negative as tangent is negative in second quadrant)

Also, we are asked to find the value of: $\tan 2x$

We know that:

$\tan 2x=\dfrac{2\tan x}{1-\tan^2 x}\\\\\\Hence,\\\\\\\tan 2x=\dfrac{2\times \dfrac{-4}{3}}{1-(\dfrac{-4}{3})^2}\\\\\\\tan 2x=\dfrac{\dfrac{-8}{3}}{1-\dfrac{16}{9}}\\\\\\\tan 2x=\dfrac{\dfrac{-8}{3}}{\dfrac{9-16}{9}}\\\\\\\tan 2x=\dfrac{\dfrac{-8}{3}}{\dfrac{-7}{9}}\\\\\\\tan 2x=\dfrac{-24}{-7}\\\\\\\tan 2x=\dfrac{24}{7}$