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Prove that : cosec^2 theta+ sin^2 theta ...

Prove that : `cosec^2 theta+ sin^2 theta` can never be less than 2.

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Prove that sec^2 theta+ cos^2 theta can never be less than 2.

Prove that : sin 2 theta= 2sin theta cos theta .

Prove that : tan^2 theta -sin^2 theta =tan^2 theta sin^2 theta .

Prove that : cos2 theta= cos^2 theta-sin^2 theta=1-2 sin^2 theta= 2 cos^2 theta-1 .

If theta be any real, prove that : cos4 theta=1-8 sin^2 theta cos^2 theta =1-8 cos^2 theta +8 cos^4 theta .

Prove that (1 +cot theta -cosec theta )(1+tan theta +sec theta )=2.

Prove that : sin^8 theta- cos^8 theta= (sin^2 theta- cos^2 theta)(1-2 sin^2 theta cos^2 theta) .

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

Prove that : (cosec theta)/(cosec theta-1)+ (cosec theta)/ (cosec theta+1)= 2 sec^2 theta .

Prove the following identity : sqrt (sec^2 theta+ cosec^2 theta)= tan theta+ cot theta= sec theta cosec theta .

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If sin theta= -1/sqrt2 and tan theta=1, find the quadrant in which the...

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  2. Prove that sectheta+costheta can never be equal to (3)/(2).

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  3. Prove that : cosec^2 theta+ sin^2 theta can never be less than 2.

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  4. Is the equation 2 cos^2 theta + cos theta-6 = 0 possible ?

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  5. Is the equation 2 sin^2 theta -cos theta+ 4 = 0 possible ?

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  6. Find the values of the remaining functions in the following problem : ...

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  7. Find the values of other five trignometrtic functions in each of the f...

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  8. Find the values of the remaining functions in the following problem : ...

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  9. Find the values of the remaining functions in the following problem : ...

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  10. Find the values of the remaining functions in the following problem : ...

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  11. Find the values of the remaining functions in the following problem : ...

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  12. Find the values of the remaining functions in the following problem : ...

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  13. Find the values of the remaining functions in the following problem : ...

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  14. Find the values of the remaining functions in the following problem : ...

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  15. If cos A=21/29 and A lies in the fourth quadrant, find sin A and tan A...

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  16. If sin A=21/29 and A lies in the second quadrant, find sec A + tan A=(...

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  17. If sin theta sec theta = -1 and theta lies in the second quadrant, f...

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  18. If cos theta cosec theta = -1 and theta lies in the fourth quadrant, ...

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  19. If sinA :cosA :: 8: 15, find sin A and cos A.

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  20. If cosec A -cot A= 3/2, find cos A and also the quadrant in which A li...

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