Question

If tan x = (cos 9 + sin 9)/(cos 9 - sin 9), then x =

Answer 1

Answer:

Correct option is

B

54o

tanθ=cos9−sin9cos9+sin9 dividing by cos 9

=1−tan91+tan9      tan45=1

=1−tan45+tan9tan45+tan9        tan(A+B)=1−tanA.TanBtanA+tanB

=tan(45+9)

tanθ=tan54

∴θ=54∘

Answer 2

Answer:

54°

Step-by-step explanation:

Given :

$\mathrm{tanx = \dfrac{cos9 + sin9}{cos9-sin9} }$

To find :

Value of x

Solution :

We know that,

$\boxed{\mathrm {\mathrm{\dfrac{cos9 + sin9}{cos9-sin9} = tan\bigg(\dfrac{\pi}{4} + x\bigg) = tan(45^{\circ} + x) }}}$

So,

$\implies \mathrm{tanx = \dfrac{cos9 + sin9}{cos9-sin9} = tan(45^{\circ} + 9^{\circ})}$

$\implies \mathrm{tanx = tan54^{\circ}}$

$\therefore \underline{\boxed{\mathrm{x = 54^{\circ}}}}$

Hope it helps!!