trigonometric functions In fact they will be valid only for some values of x for which inverse trigonometric functions are defined We will not go into the details of these values of x in the domain as this discussion goes beyond the scope of this textbook Let us recall that sin x then x sin y and if x sin y then y sin x This is equivalent to For suitable values of domain similar results follow for remaining trigonometric functions 28 sin sin x x x 1 1 and sin sin x x x E 2 MATHEMATICS We now consider some examples Example 3 Show that 1 sin 2x 1 x 2 sin X 1 ii sin 2x 1 x 2 cos x Solution tan Rationalised 2023 24 i Let x sin 0 Then sinx 0 We have 1 Example 4 Express tan Solution We write 25x5 1 2 x 2 sin 2x 1 x sin 2 sin 0 1 sin 0 COS X 1 sinx ii Take x cos 0 then proceeding as above we get sin tan x 1 not sin 2sine cos0 sin sin2 2 sin x 2 COS 2 2 X 2 X 2 sin COS X 2 2 X X cos sin COS sin 2 x 2 sin the simplest form t to be reputasted x 2 cos x