Question

Factor the algebraic expression below in terms of a single trigonometric function. sin 2x + sin x - 2

Answer 1

Answer:

The factored form is (sin x +2)(sin x-1)

Step-by-step explanation:

We have been given the trigonometric function $\sin^2 x +\sinx-2$

We can factor this by AC method. In AC method we multiply the term a and c and then write the middle term b in such a way that the sum/difference is equal to the product 'ac'

Using the method, we can write sinx as 2sinx -sinx

$\sin^2 x +2\sinx-\sin x-2$

Now, we group the first two terms and the last two terms

$(\sin^2 x +2\sinx)+(-\sin x-2)$

Now, we take GCF from each group

$\sin x(\sin x +2)-1(\sin x+2)$

Factor out (sinx+2)

$(\sin x +2)(\sin x-1)$

Therefore, the factored form is (sin x +2)(sin x-1)

Answer 2

Answer:

The factor form is $(\sin x+2)(\sin x-1)$

Step-by-step explanation:

Given : Algebraic expression $\sin^2x+\sin x-2$

To find : Factor the algebraic expression in terms of a single trigonometric function ?

Solution :

Algebraic expression $\sin^2x+\sin x-2$

Let $\sin x=y$

So, $y^2+y-2$

To factor the expression we equate it to zero,

$y^2+y-2=0$

Apply middle term split,

$y^2+2y-y-2=0$

$y(y+2)-1(y+2)=0$

$(y+2)(y-1)=0$

Substitute the value of y, $y=\sin x$

$(\sin x+2)(\sin x-1)=0$

The factor form is $(\sin x+2)(\sin x-1)$