What is the value Of this

(sinA-cosA+1)/(sinA+cosA-1)=2(1+cosecA)

borishaifa [10]

Answer:

The trigonometrical expression is sin² A + sin A - 2 cos A - 2 cos A × sin A = 0

Step-by-step explanation:

Given Trigonometrical function as :

$\frac{sin A - cos A + 1}{sin A + cos A - 1}$ = 2 (1 + cosec A)

Or, $\frac{sin A + ( 1 - cos A)}{sin A - (1 - cos A)}$ = 2 (1 + cosec A)

,<u> Now, rationalizing </u>

$\frac{(sin A + ( 1 - cos A)) \times (sin A + (1 - cosA))}{(sin A - (1 - cos A))\times (sin A + (1 - cos A))}$ = 2 (1 + cosec A)

Or, $\frac{(sin A + (1 - cos A))^{2}}{sin^{2} - (1-cos A)^{2}}$ = 2 ( 1 + $\dfrac{1}{\textrm sinA}$

Or, $\frac{sin^{2}A + (1 - cosA)^{2} + 2 \times sin A \times (1 - cos A)}{sin^{2}A - (1 + cos^{2}A - 2 cos A)}$ = 2 ( $\dfrac{1 + sin A}{sin A}$

Or, $\frac{sin^{2}A + 1 + cos^{2}A - 2 cos A + 2 sin A - 2 sin A cos A}{sin^{2}A - 1 - cos^{2}A +2 cos A}$ = 2 ( $\dfrac{1 + sin A}{sin A}$

Or, $\frac{sin^{2}A + 1 + cos^{2}A - 2 cos A + 2 sin A - 2 sin A cos A}{sin^{2}A - (sin^{2}A + cos^{2}A) - cos^{2}A +2 cos A}$ = 2 ( $\dfrac{1 + sin A}{sin A}$

Or, $\frac{2- 2 cos A + 2 sin A - 2 sin A cos A}{- 2cos^{2}A +2 cos A}$ = 2 ( $\dfrac{1 + sin A}{sin A}$

Or, $\frac{1- cos A + sin A - sin A cos A}{- cos^{2}A + cos A}$ = 2 ( $\dfrac{1 + sin A}{sin A}$

Or, $\frac{(1- cos A) + sin A (1-cos A)}{cos A(1 - cos A)}$ = 2 ( $\dfrac{1 + sin A}{sin A}$

Or, $\frac{(1- cos A) (1 + sinA)}{cos A(1 - cos A)}$ = 2 ( $\dfrac{1 + sin A}{sin A}$

Or, $\frac{(1 + sinA)}{(cos A)}$ = 2 ( $\dfrac{1 + sin A}{sin A}$

Or, sin A + sin² A = 2 cos A (1 + sin A)

Or, sin A + sin² A = 2 cos A + 2 cos A × sin A

Or, sin² A + sin A - 2 cos A - 2 cos A × sin A = 0

So,The trigonometrical expression is sin² A + sin A - 2 cos A - 2 cos A × sin A = 0 Answer

6 0

3 years ago

The directrix of a parabola is y=−4y=−4 . The focus of the parabola is (−2,−2)(−2,−2) .

Dennis_Churaev [7]

Because the focus is (-2,-2) and the directrix is y = -4, the vertex is (-2,-3).

Consider an arbitrary point (x,y) on the parabola.
The square of the distance between the focus and P is
(y+2)² + (x+2)²
The square of the distance from the point to the directrix is
(y+4)²

Therefore
(y+4)² = (y+2)² + (x+2)²
y² + 8y + 16 = y² + 4y + 4 + (x+2)²
4y = (x+2)² - 12
y = (1/4)(x+2)² - 3

Answer: $y= \frac{1}{4} (x+2)^{2} - 3$

5 0

3 years ago

Simplify 2(x - 3) + 7(x + 2).

harkovskaia [24]

The answer is 9x + 8.

4 0

4 years ago

Read 2 more answers

Help me pls giving 25 points

ankoles [38]

The answer to this question is Letter B.

4 0