Question

Question 8: Write the function in the simplest form: tan¯¹ (cosx - sin x/cos x + sin x) , x < π

Class 12 - Math - Inverse Trigonometric Functions

Answer 1

Hey there!!!

=> tan¯¹ (cosx - sin x/cos x + sin x) , x < π

Dividing numerator and denominator by cosx→
=> tan¯¹ [ ( 1 - sinx/cosx) / (1 + sinx/cosx) ]
=> tan¯¹ ( 1-tanx / 1+tanx )

we know, tan¯¹(x-y / 1+xy) = tan¯¹x - tan¯¹y

So,

=> tan¯¹ (1) - tan¯¹ (tanx)
=> π/4 - x


Hope it helps.....✌