## Solving how to verify trigonometric identities

Introduction :

Verify trigonometric identities are included in both trigonometric functions and single variables. Generally, this is identities are included one or more angles. This is identities are involved that the length and angles of the triangle. Identities are both sides are equal and both angles are equals. Trigonometric identities are three basic identities are used.

Examples to solving how to verify trigonometric identities:

solving example 1:

How to solving verify identity that cos A * tan A = sin A

Solution:

Use the identity tan A = `sin A / cos A` in the left side.

cos A x tan A = cos A x (`sin A / cos A` )

= sin A

solving example 2:

how to solving verify the identity cot A x sec A x sin A = 1

Solution:

Use the identities cot A =` cos A / sin A` and sec A = `1/ cos A ` in the left side.

cot A x sec A x sin A = `(cos A / sin A)` x `(1/ cos A)` x sin A

`(cos A / sin A)`x ` (1/ cos A) ` x sin A

= 1

solving trigonometric identities example 3:

verify the identity` [ cot A - tan A ] / [sin Axx cos A]` = csc2 A - sec2A

Solution to Example 3 :

Take LHS:

We use the identities cot A = `cos A / sin A` and tan A =` sin A / cos A` to transform the left side as follow.

`[ cot A - tan A ] / [sin Axx cos A] ` = `[(cos A / sin A) - (sin A / cos A)] / [sin A xxcos A] `

=` [{(cos ^2A) -(sin^ 2A)} / (cos Axx sin A)] / [sin Axx cos A] `

= `[cos^ 2A - sin ^2A] / [sin Axx cos A]^2 ` (expression 1) -------------------(1)

Take RHS:

We now transform the right side using the identities csc A = `1 / sin A ` and sec A = `1 / cos A` .

csc2A - sec2A = `(1/sin A)^2 - (1/ cos A)^2`

csc 2A – sec2A = `(1/(sin^2A)) - (1/(cos^2A))`

=` (cos^2A-sin^2A)/(sin^2A xx cos^2A)`

=` [ cos^2A - sin^2A ] / [sin Axx cos A]^2` (expression 2) ---------------------(2)

(1) = (2)

LHS = RHS

Verify trigonometric identities are included in both trigonometric functions and single variables. Generally, this is identities are included one or more angles. This is identities are involved that the length and angles of the triangle. Identities are both sides are equal and both angles are equals. Trigonometric identities are three basic identities are used.

Examples to solving how to verify trigonometric identities:

solving example 1:

How to solving verify identity that cos A * tan A = sin A

Solution:

Use the identity tan A = `sin A / cos A` in the left side.

cos A x tan A = cos A x (`sin A / cos A` )

= sin A

solving example 2:

how to solving verify the identity cot A x sec A x sin A = 1

Solution:

Use the identities cot A =` cos A / sin A` and sec A = `1/ cos A ` in the left side.

cot A x sec A x sin A = `(cos A / sin A)` x `(1/ cos A)` x sin A

`(cos A / sin A)`x ` (1/ cos A) ` x sin A

= 1

solving trigonometric identities example 3:

verify the identity` [ cot A - tan A ] / [sin Axx cos A]` = csc2 A - sec2A

Solution to Example 3 :

Take LHS:

We use the identities cot A = `cos A / sin A` and tan A =` sin A / cos A` to transform the left side as follow.

`[ cot A - tan A ] / [sin Axx cos A] ` = `[(cos A / sin A) - (sin A / cos A)] / [sin A xxcos A] `

=` [{(cos ^2A) -(sin^ 2A)} / (cos Axx sin A)] / [sin Axx cos A] `

= `[cos^ 2A - sin ^2A] / [sin Axx cos A]^2 ` (expression 1) -------------------(1)

Take RHS:

We now transform the right side using the identities csc A = `1 / sin A ` and sec A = `1 / cos A` .

csc2A - sec2A = `(1/sin A)^2 - (1/ cos A)^2`

csc 2A – sec2A = `(1/(sin^2A)) - (1/(cos^2A))`

=` (cos^2A-sin^2A)/(sin^2A xx cos^2A)`

=` [ cos^2A - sin^2A ] / [sin Axx cos A]^2` (expression 2) ---------------------(2)

(1) = (2)

LHS = RHS