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

Hence, the value of tan2x is:

24/7

Explanation:

We are given sine trignometric ratio as:

`\sin x=(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=(P)/(B)\\\\i.e.\\\\\tan x=-(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=(2\tan x)/(1-\tan^2 x)\\\\\\Hence,\\\\\\\tan 2x=(2* (-4)/(3))/(1-((-4)/(3))^2)\\\\\\\tan 2x=((-8)/(3))/(1-(16)/(9))\\\\\\\tan 2x=((-8)/(3))/((9-16)/(9))\\\\\\\tan 2x=((-8)/(3))/((-7)/(9))\\\\\\\tan 2x=(-24)/(-7)\\\\\\\tan 2x=(24)/(7)`