Class 12 Maths Inverse Trigonometric Functions Domain & range of inverse functions

Domain & range of inverse functions

 

 

Numerical: Find sin–1 (-1/2)

Solution: sin–1 (-1/2) =y

Sin y = -1/2   = sin (-π/6)

Or  y = -π/6

 

Properties of Inverse Trigonometric Functions

 

 

Numerical: Prove that 2 tan-1 ½ +  tan-1 1/7 = tan-1 31/17

Solution: LHS =  2 tan-1 ½ +  tan-1 1/7

= tan-1 [ (2 * ½)/ 1- (1/2)2)]    +  tan-1 1/7 

= tan-1(4/3) +  tan-1 1/7

= tan-1[( 4/3 + 1/7)/(1 – 4/3 * 1/7]

= tan-1 [31/17]   = RHS

 

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