Verify the identity cosx cos(-x) - sinx sin(-x) =1

(identity has been verified)

Step-by-step explanation:

Verify the following identity:

cos(x) cos(-x) - sin(x) sin(-x) = 1

Hint: | Cosine is an even function.

Use the identity cos(-x) = cos(x):

cos(x) cos(x) - sin(-x) sin(x) = ^?1

Hint: | Sine is an odd function.

Use the identity sin(-x) = -sin(x):

cos(x) cos(x) - -sin(x) sin(x) = ^?1

Hint: | Evaluate cos(x) cos(x).

cos(x) cos(x) = cos(x)^2:

cos(x)^2 - ( - sin(x) sin(x)) = ^?1

Hint: | Evaluate -(-sin(x)) sin(x).

-(-sin(x)) sin(x) = sin(x)^2:

cos(x)^2 + sin(x)^2 = ^?1

Hint: | Use the Pythagorean identity on cos(x)^2 + sin(x)^2.

Substitute cos(x)^2 + sin(x)^2 = 1:

1 = ^?1

Hint: | Come to a conclusion.

The left hand side and right hand side are identical:

(identity has been verified)

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

60°

step-by-step explanation:

the measure angle of c in an isosceles triangle abc is 60° because in isosceles triangle,the measures of all the angles is 60°.