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Prove the following identities, where th...

Prove the following identities, where the angles involved are acute angles for which the expressions are defined. : `(sin A + cosec A)^2+(cosA+secA)^2=7+tan^2A+cot^2A` .

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MBD-INTRODUCTION TO TRIGONOMETRY-EXERCISE
  1. Prove the following identities, where the angles involved are acute an...

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  2. In triangleABC, right angled at A, if AB = 12 cm, AC = 5 cm and BC = ...

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  3. In triangleOPQ, right angled at P, OP = 7 cm and OQ - PQ = 1 cm. Deter...

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  4. If sintheta=sqrt3costheta , find all the six T-ratios..

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  5. If sin A = 1/3 evaluate the cos A cosec A + tan A sec A.

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  6. If tantheta=12/5, calculate sintheta , costheta and verify sin^2theta+...

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  7. If tan A = sqrt2-1 show that (tanA)/(1+tan^2A)=(sqrt2)/4 = sinA cos A...

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  8. If sec theta=5/4 verify that (tantheta)/(1+tan^2theta)=(sintheta)/(sec...

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  9. If sin B=1/2 find the value of 3 cosB-4cos^3B .

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  10. In a right angled triangle ABC, right angled at B, if tan A = 1, then ...

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  11. If cottheta=3/4 prove that sqrt((sectheta-cosectheta)/(sectheta+cosec...

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  12. If tan theta=3/4 , show that sqrt((1-sintheta)/(1+sintheta))=1/2 .

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  13. In triangleABC , right angle at C, if tan A =1/sqrt3. Show that sin A...

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  14. If cosec A = 2 , find the value of 1/(tan A)+(sinA)/(1+cosA).

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  15. If cot B=12/5 Prove that tan^2B-sin^2B=sin^4B.sec^2B .

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  16. If tantheta+(1)/(tantheta)=2 , find the value of tan^2theta+(1)/(tan^2...

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  17. If 3cos theta-4sintheta=2costheta+sintheta find tantheta .

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  18. If sintheta=3/5, evaluate [(costheta-(1/tantheta))/(2cottheta)] .

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  19. What is the value of sina . .

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  20. If A=30^@ verify that :- cos2A= (1-tan^2A)/(1+tan^2A) .

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  21. If A=30^@ verify that :- cos2A= cos^2A-sin^2A .

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