Prove that (1+tan^2 A)+(1+1/tan^2 A) = 1/(sin^2 A-sin^4A)

 

P. Prove that (1+tan^2 A)+(1+1/tan^2 A) = 1/(sin^2 A-sin^4A)

(AP 2017 Public Exam Question)

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1. If cosecA+ cotA=k then prove that cosA=(k^2-1)/(k^2+1)

2. Show that (cosecA-cotA)^2=(1-cosA)/(1+cosA)|(sinA+cosecA)^2+(cosA+secA

3. Prove that (1+tan^2 A)+(1+1/tan^2 A) = 1/(sin^2 A-sin^4A)

4. A tree breaks due to storm and the broken part bends

5. The angles of elevation of the top of a tower from two points at

6. Prove that (sinA-cosecA)^2+(cosA-secA)^2=(cot^2)A+(tan^2)A-1

7. Two poles of equal heights are standing opposite to each other on either

8. In ∆ABC and ∆XYZ, if angleA and angle X are acute angles such that cosA=cosX then

9. Given DE||BC, AD=4.5cm, BD=9cm and EC=8cm

10. In a right angle triangle ABC, right angle is at B, if tanA=√3, then find the

11. In ∆XYZ, right angle is at Y, YZ=x and XZ=2x then determine angleYXZ

12. Prove that (sinA-cosA+1)/(sinA+cosA-1)=1/(secA-tanA)

13. If tanA=5/12, then find secA and cosecA

14. In triangle ABC LM||BC AL/LB=2/3, AM=5. Find AC

15. Prove that 1+tan^2(A)/1+cot^2(A)=(1+tanA)/(1+cotA)

16. If cosecA+cotA=2 then find cosA|Prove that (1+secA)/secA=(sin^2A)/(1-cosA)

17. Prove that (cotA-cosA)/(cotA+cosA)=(cosecA-1)/(cosecA+1)

18. Two angles are complementary and one angle is 18°

19. If cosec theta+cot theta =k then prove that cos theta=

20. Show that (cosec theta - cot theta)^2=(1-cos theta)/

21. Prove that (sin theta+cosec theta)^2+(cos theta+sec theta)^2

22. Prove that (1+tan^2 theta)+(1+1/tan^2 theta)=1/

23. If 4sin^2 theta-1=0 then find theta (theta less than 90)

24. Prove that (sin theta-cosec theta)^2+(cos theta-sec theta)^2=

25. In a right angle triangle ABC, right angle is at B

26. find the value of cosA.cosC-sinA.sinC

27. Prove that sin theta-cos theta+1 by sin theta+cos theta-1=1 by

28. Prove that (1+sec theta)/sec theta=sin square theta/(1-cos theta)

29. Prove that (cosecA-sinA).(secA-cosA)=1/(tanA+cotA)

30. If cosA=7/25, find sinA and cosecA. What do you observe

31. The length of shadow of a pole is equal to the length of the pole