Prove that (〖sin〗^2 θ)/(1+cosθ)=1-cosθ

proved

Step-by-step explanation:

prove that : (sin^2 θ)/(1+cosθ)=1-cosθ

(sin^2θ)*(1−cosθ)/(1+cosθ)(1+cosθ) =

sin^2Ф)(1-cosФ)/1-cos^2Ф since 1-cos^2Ф=sin^2Ф then:

(sin^2Ф)(1-cosФ)/sin^2Ф =

1-cosФ     (sin^2Ф/sin^Ф=1)

proved

a) D. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

b) C. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Step-by-step explanation:

a) We have a hypothesis test with the following hypothesis:

The significance level is 0.05 for this right-tailed test.

The sample size is n=17.

This means we have 16 degrees of freedom.

The test statistic has already been calculated and has a value of t=3.1.

This test is a right-tailed test, with 16 degrees of freedom and t=3.1, so the P-value for this test is calculated as (using a t-table):

As the P-value (0.0034) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to support the claim that the new paint has a reflectometer reading higher than 20.

b. The hypothesis are the same as point a:

The degrees of freedom for this sample size are:

The significance level is 0.01.

The test statistic has already been calculated and has a value of t=1.8.

This test is a right-tailed test, with 9 degrees of freedom and t=1.8, so the P-value for this test is calculated as (using a t-table):

As the P-value (0.0527) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the new paint has a reflectometer reading higher than 20.