Question

If 4k = tan² 60° − 2 cosec² 30° − 2 tan² 30°, then find the value of k.

Answer 1

Given:

4k = tan² 60° − 2 cosec² 30° − 2 tan² 30°

Step 1: Find the values of trigonometric functions

• `tan^2 60^@ = sqrt3`
  `tan^2 60^@ = 3`
• `"cosec"  30^@ = 2`
  `"cosec"^2  30^@ = 4`
• `tan 30^@ = 1/(sqrt3)`
  `tan^2 30^@ = 1/3`

Step 2: Substitute the values

`4k = 3 - 2(4) - 2 (1/3)`

`4k = 3 - 8 - 2/3`

`4k = -5 - 2/3`

`4k = (-15 - 2)/(3) = (-17)/3`

Step 3: Solve for k

`k = (-17)/12`