Question

1 - sin squared theta divided by 1 + cos theta is equal to​

Answer 1

Answer:

1-costheta

Step-by-step explanation:

sin2theta/1+costheta

(1-cos2theta)/1+costheta

(1+costheta)(1-costheta)/1+costheta

1-costheta

Answer 2

The  value  of  the  given expression  $1-\frac{\sin^2\theta}{1+\cos\theta}$ is $\cos\theta$

Therefore  $1-\frac{\sin^2\theta}{1+\cos\theta}=\cos\theta$

Step-by-step explanation:

Given expression is $1-\frac{\sin^2\theta}{1+\cos\theta}$

To find the value of the given expression :

• $1-\frac{\sin^2\theta}{1+\cos\theta}$

• $=\frac{1(1+\cos\theta)-\sin^2\theta}{1+\cos\theta}$ ( here taking LCM $1+\cos\theta$ )

• $=\frac{1+\cos\theta-sin^2\theta}{1+\cos\theta}$
• $=\frac{\cos\theta+(1-sin^2\theta)}{1+\cos\theta}$
• $=\frac{\cos\theta+(\cos^2\theta)}{1+\cos\theta}$ ( here by using the identity $\cos^2\theta=1-sin^2\theta$)
• $=\frac{\cos\theta(1+\cos\theta)}{1+\cos\theta}$

• $=\cos\theta$ ( here $1+\cos\theta$ getting cancelled )
• Therefore  $1-\frac{\sin^2\theta}{1+\cos\theta}=\cos\theta$

The  value of  the  given  expression  $1-\frac{\sin^2\theta}{1+\cos\theta}$  is  $\cos\theta$