Question

Can someone help me with these trig problems?

Answer 1

40)

Step 1:

The trigonometric identity is .

Left hand side identity =

Apply reciprocal identities .

Apply Pythagorean identity .

= Right hand side identity.

Solution:

.

Answer 2

73)

Step 1:

The The trigonometric identity is .

Left hand side identity =

Apply the formula difference of two squares .

In this case .

Apply Pythagorean identity .

= Right hand side identity.

Solution:

.

Answer 3

81)

Step 1:

The trigonometric identity is .

Left hand side identity

Apply the formula .

Apply reciprocal identity .

Apply Pythagorean identities and .

= Right hand side identity.

Solution:

.

Answer 4

85)

Step 1:

The trigonometric identity is .

Left hand side identity =

Apply the formula .

In this case .

Apply Pythagorean identity .

= Right hand side identity.

Solution:

.

Answer 5

55)

Step 1:

The trigonometric identity is .

 Left hand side identity =

Apply quotient identity .

Apply Pythagorean identity .

= Right hand side identity.

Solution:

.

Answer 6

94)

Step 1:

The rational expression is .

Substitute in above expression.

Apply Pythagorean identity .

Apply quotient identity .

.

Solution:

.

Answer 7

102)

Step 1:

Observe figure,  the triangle is a right angle triangle.

A right angle triangle is a triangle in which one angle is a right angle(that is a angle).

The relation between the sides and angles of a right angle is the basis for trigonometry.

Sum of three interior angles of any triangle is .

In given triangle one angle is right angle, so remaining two angles add to .

Therefore, the angle .

Step 2:

Since is in first quadrant, the six trigonometric functions are positive.

.