Answer the following questions using what youve learned from

Answer the following questions using what you\'ve learned from this unit. write your resp space provided. For questions 1 5, decide whether the equation is a trigonometric identity. Explain your reaso 1. cos2 x(1 +tan2x) 1 (3 points) 2. sec xtanx(1- sin2 x) sin x (3 points)

Solution

1. cos²x(1+ tan²x)=1

Starting with the left side

cos²x(1+tan²x)

cos²x + sin²x=1 That is the right side

2. sec x ta x (1-sin²x)=sin x

Starting with left side

We have to use the following identity

1-sin²c=cos²x

sec tanx * cos²x   = (1/cos x)(sin x/cos x)*cos²x = sinx that is the right side

3. csc x(2sinx - sqrt2)=0

csc x(2sinx)- sqrt2 cos x

2- sqrt2 cos x

That is not equal to right side . So its not an identity.