Question

Tan theta cosec 2 theta - tan theta is equal to dash

Answer 1

Given: ( tan Ф cosec 2 Ф ) - tan Ф

To find: Find the value of the given trigonometric expression.

Solution:

• As we have given the expression tan Ф cosec 2 Ф - tan Ф, first we need convert all terms in sin Ф and cos Ф.

              (sin Ф/ cosФ x 1 / sin 2Ф) - (sin Ф/cos Ф)

• Now solving the terms, we get:

              (sin Ф/ cosФ x 1/ 2 sin Ф cos Ф) -  (sin Ф/cos Ф)

              (1/ 2 cos²Ф) - (sin Ф/cos Ф)

              (1/ 2 cos²Ф) - (2 cos Ф sin Ф/ 2 cos²Ф)

              1 - sin 2Ф / 2 cos²Ф

• Now we can write 1 - sin 2Ф as (sin Ф - cos Ф)².

• So putting this in above expression, we get:

             (sin Ф - cos Ф)² / 2 cos²Ф

             1/2 (sin Ф - cos Ф / cos Ф)²

             1/2 ( tan Ф - 1 )²

Answer:

          So the value of tan Ф cosec 2 Ф - tan Ф is   1/2 ( tan Ф - 1 )².

Answer 2

Answer:

Step-by-step explanation: