verify that tan^2 x -sin^2 x = sin^2 x tan^2 x is an identity by substituting in x=pi/6

Question

No clue how to start or answer the problem. The question is supposed to be shown in exact values.

Answer 1

π/6 = 30°

tan30° = sin30° / cos30° = (1/2) / (√3 / 2) = 1 / √3

Left hand side:

tan²30° - sin²30° = (1 / √3)² - (1/2)² = 1/3 - 1/4 = 1/12

Right hand side:

(sin²30°)(tan²30°) = (1/2)² (1 / √3)² = (1/4)(1/3) = 1/12

The 2 sides give the same value.