Class 12 Maths NCERT Miscellaneous Exercise | Chapter 2 Inverse Trigonometric Functions

Class 12 Maths NCERT Miscellaneous Exercise

1. cos^(-1)⁡(cos⁡(13pi/6) )

2. tan^(-1)⁡(tan⁡(7pi/6) )

3.

4. [sin]^(-1)⁡[8/17]+[sin]^(-1)⁡[3/5]=[tan]^(-1)⁡[77/36]

5. [cos]^(-1)⁡[4/5]+[cos]^(-1)⁡[12/13]=[cos]^(-1)⁡[33/65]

6. [cos]^(-1)⁡[12/13]+[sin]^(-1)⁡[3/5]=[sin]^(-1)⁡[56/65]

7. [tan]^(-1)⁡[63/16]=[sin]^(-1)⁡[5/13]+[cos]^(-1)⁡[3/5]

8. [tan]^(-1)⁡[1/5]+[tan]^(-1)⁡[1/7]+[tan]^(-1)⁡[1/3]+[tan]^(-1)⁡[1/8]=pi/4

9. [tan]^(-1)⁡sqrtx=1/2 [cos]^(-1)⁡((1-x)/(1+x)),x∈[0,1]

10. [cot]^(-1)⁡((sqrt(1+sin⁡x )+sqrt(1-sin⁡x ))/(sqrt(1+sin⁡x )-sqrt(1-sin⁡x )))=x/2

11. [tan]^(-1)⁡((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=pi/4-1/2 [cos]^(-1)⁡x

12. 9pi/8-9/4 [sin]^(-1)⁡[1/3]=9/4 [sin]^(-1)⁡[(2sqrt2)/3]

13. 2 [tan]^(-1)⁡( cos⁡x)=[tan]^(-1)⁡( 2"cosec" x)

14. [tan]^(-1)⁡[(1-x)/(1+x)]=1/2 [tan]^(-1)⁡x,

15. sin⁡( tan^(-1)⁡x ),

16. [sin]^(-1)⁡( 1-x)-2 [sin]^(-1)⁡x=pi/2

17. tan^(-1)⁡(x/y)-tan^(-1)⁡((x-y)/(x+y))

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