The 1-sinx formula is given by 1-sinx= [cos(x/2) -sin(x/2)]2. The 1 plus sinx idenity is given as follows:
$1+\sin x =(\cos \frac{x}{2}+\sin \frac{x}{2})^2$.
Let us now find the formula of 1-sinx and 1+sinx.
Formula of 1-sinx
Answer: 1-sinx= $(\cos \frac{x}{2}-\sin \frac{x}{2})^2$.
Explanation:
To find the formula of 1-sinx, we will use the following two trigonometric identities:
- cos2θ +sin2θ = 1
- sin2θ = 2sinθ cosθ
So the given expression 1-sinx can be written as
1- sinx
= cos2 $\frac{x}{2}$ +sin2 $\frac{x}{2}$ – 2sin $\frac{x}{2}$ cos $\frac{x}{2}$
= $(\cos \frac{x}{2}-\sin \frac{x}{2})^2$, here we have used the formula: a2+b2 -2ab=(a-b)2.
So the formula of 1-sinx is equal to [cos(x/2) -sin(x/2)]2.
Also Read: 1-cosx Formula, Identity with Proof
Sin3x formula in terms of sinx
Formula of 1+sinx
Answer: 1+sinx is equal to $(\cos \frac{x}{2}+\sin \frac{x}{2})^2$.
Explanation:
As before, we have that
1+ sinx
= cos2 $\frac{x}{2}$ +sin2 $\frac{x}{2}$ + 2sin $\frac{x}{2}$ cos $\frac{x}{2}$
= $(\cos \frac{x}{2}+\sin \frac{x}{2})^2$, using the formula: a2+b2 +2ab=(a+b)2.
Therefore, the formula of 1+sinx is equal to [cos(x/2) + sin(x/2)]2.
Read Also: cot(a+b)cot(a-b) Formula
FAQs
Q1: What is the formula of 1+sinx?
Answer: The formula of 1+sinx is given by 1+sinx= [cos(x/2) +sin(x/2)]2.