Question

if 0°<x<90° and 2sinx+15cos²x=7, then the value of tan x is​

Answer 1

EXPLANATION.

⇒ 0° < X < 90°.

⇒ 2sinx + 15cos²x = 7.

As we know that,

Formula of :

⇒ sin²x + cos²x = 1.

⇒ cos²x = 1 - sin²x.

Using this formula in the equation, we get.

⇒ 2sinx + 15(1 - sin²x) = 7.

⇒ 2sinx + 15 - 15sin²x = 7.

⇒ 7 - 15 + 15sin²x - 2sin x = 0.

⇒ 15sin²x - 2sinx - 8 = 0.

⇒ 15sin²x - 12sinx + 10sin x - 8 = 0.

⇒ 3sinx(5sinx - 4) + 2(5sinx - 4) = 0.

⇒ (3sinx + 2)(5sinx - 4) = 0.

⇒ 3sinx + 2 = 0.

⇒ sin x = -2/3 [Rejected].

⇒ 5sinx - 4 = 0.

⇒ sin x = 4/5.

As we know that,

⇒ cos²x = 1 - sin²x.

⇒ cos²x = 1 - (4/5)².

⇒ cos²x = 1 - (16/25).

⇒ cos²x = (25 - 16)/25.

⇒ cos²x = 9/25.

⇒ cos x = √(9/25).

⇒ cos x = 3/5.

⇒ tan x = (sin x)/(cos x).

⇒ tan x = (4/5)/(3/5).

⇒ tan x = 4/5 x 5/3.

⇒ tan x = 4/3.

                                                                                                                       

MORE INFORMATION.

(1) sin²x + cos²x = 1.

(2) 1 + tan²x = sec²x.

(3) 1 + cot²x = cosec²x.

Answer 2

Answer:

Ans = 4/3

Step-by-step explanation:

$2sinx+15cos^2 x=7 \\ 2sinx+15(1−sin^2 x)−7=0 \\ 2sinx−15sin^2 x+8=0 \\ 15sin^2 x−2sinx−8=0$$sin \: x = \frac{2± \sqrt{4+4.15.8} }{2.15} \\ = \frac{2± \sqrt{4+480} }{30} \\ = \frac{2±22}{30} \\ = \frac{24}{30} , \frac{ - 20}{30} \\ sin \: x>0 ( \therefore0<x<90 \degree) \\ sin \: x = \frac{24}{30} = \frac{4}{5} \\ cos \: x = \sqrt{1 - \frac{16}{25} } = \sqrt{ \frac{9}{25} } = \frac{3}{5} \\ tan \: x = \frac{sin \: x}{cos \: x} = \frac{4/5}{3/5} = \frac{4}{3} \\ \therefore \: tan \: x = \frac{4}{3}$