If sin- - cos- -15- then tan -2 satisfies which of the following equation -

Find the discriminant of each of the following equations :
(i) $2 x^{2} - 7 x + 6 = 0$ (ii) $3 x^{2} - 2 x + 8 = 0$
(iii) $2 x^{2} - 5 \sqrt{2} x + 4 = 0$ (iv) $\sqrt{3} x^{2} + 2 \sqrt{2} x - 2 \sqrt{3} = 0$
(v) $(x - 1) (2 x - 1) = 0$ (vi) $1 - x = 2 x^{2}$

Find the equation of the circle which cuts the following circles orthogonally.
$x^{2} + y^{2} + 2 x + 4 y + 1 = 0,$
$2 (x^{2} + y^{2}) + 6 x + 8 y - 3 = 0,$
$x^{2} + y^{2} - 2 x + 6 y - 3 = 0$

Q. If

{cos}^{- 1} x = α, (0 < x < 1)

and

{sin}^{- 1} (2 x \sqrt{1 - x^{2}}) + {sec}^{- 1} (\frac{1}{2 x^{2} - 1}) = \frac{2 π}{3}

, then

{tan}^{- 1} (2 x)

is equal to

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If sinθ+cosθ=−15, then tan θ2 satisfies which of the following equation ?

The correct option is B 2x2−5x−3=0sinθ+cosθ=−15⇒2tanθ21+tan2θ2+1−tan2θ21+tan2θ2=−15⇒2tan2θ2−5tanθ2−3=0Hence, option 'D' is correct.Let tanθ2=x∴2x2−5x−3=0

If $sin θ + cos θ = - \frac{1}{5}$ , then tan $\frac{θ}{2}$ satisfies which of the following equation ?