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Wednesday, May 16, 2018

CBSE CLASS 12 INVERSE TRIGONOMETRIC FUNCTIONS IMPORTANT QUESTIONS PDF

INVERSE TRIGONOMETRIC FUNCTIONS CLASS 12 IMPORTANT QUESTIONS

Class 12 Inverse Trigonometry important questions

Inverse Trigonometric Functions Class 12 Important Questions PDF

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1. Evaluate the following :
i) sin 1 ( sin π 4 )               ii) cos 1 ( cos 2π 3 )          iii) tan 1 ( tan π 3 ) iv) sin 1 ( sin 2π 3 )           v) cos 1 ( cos 7π 6 )           vi) tan 1 ( tan 2π 3 ) vii) cos( cos 1 ( 3 2 )+ π 6 )    viii) sin 1 ( sin( 600 o ) ) ix)cos 1 ( cos( 680 0 ) )

2. Express in the simplest form:
i) tan 1 ( cosx 1sinx ), π 2 <x< π 2 ii) tan 1 ( cosxsinx cosx+sinx ), π 4 <x< π 4

3. Prove that :
i) cot 1 { 1+sinx + 1sinx 1+sinx 1sinx }= x 2 ,0<x< π 2 ii) cot 1 { 1+sinx + 1sinx 1+sinx 1sinx }= π 2 x 2 , π 2 <x<π iii) tan 1 { 1+x 1x 1+x + 1x }= π 4 1 2 cos 1 x,0<x<1

4.Prove that :
tan 1 { 1+ x 2 + 1 x 2 1+ x 2 1 x 2 }= π 4 + 1 2 cos 1 x 2 ,1<x<1

5. Simplify each of the following :
i)  cos 1 ( 3 5 cosx+ 4 5 sinx ),where - 3π 4 x π 4 ii) sin 1 ( 5 13 cosx+ 12 13 sinx )

6. Simplify each of the following :
i) sin 1 ( sinx+cosx 2 ), π 4 <x< π 4 ii) cos 1 ( sinx+cosx 2 ), π 4 <x< 5π 4 iii)sin 1 ( sinx+cosx 2 ), π 4 <x< 5π 4 iv)cos 1 ( sinx+cosx 2 ), 5π 4 <x< 9π 4

7. Evaluate :
i) sin( cot 1 x ) ii) cos( tan 1 x ) iii) cos( sin 1 1 4 + sec 1 4 3 ) iv) sin[ cot 1 { cos( tan 1 x ) } ]

8. Prove that :
i) tan 2 ( sec 1 2 )+ cot 2 ( cose c 1 3 )=11 ii)cos[ tan 1 { sin( cot 1 x ) } ]= x 2 +1 x 2 +2 iii)cos( sin 1 3 5 + cot 1 3 2 )= 6 5 13

9. Find the value of
cot( tan 1 a+ cot 1 a )

10. If 1x,y1  such that sin 1 x+ sin 1 y= π 2 ,  find the value of cos 1 x+ cos 1 y

11. If tan 1 x cot 1 x= tan 1 1 3 , find the value of x.

12. If sin( sin 1 1 5 + cos 1 x )=1, then find the value of x.

13. Solve : sin{ sin 1 1 5 + cos 1 x }=1

14. Prove that : tan 1 1+ tan 1 2+ tan 1 3=π

15.Prove that : sin 1 12 13 + cos 1 4 5 + tan 1 63 16 =π sin 1 12 13 + cos 1 4 5 + tan 1 63 16 =π

16. Prove that : tan 1 1 2 + tan 1 1 5 + tan 1 1 8 = π 4

17. Prove that : tan 1 1 5 + tan 1 1 7 + tan 1 1 3 + tan 1 1 8 = π 4




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