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Prove the following identities : sec^(...

Prove the following identities :
`sec^(2)theta-cos^(2)theta=sin^(2)theta(sec^(2)theta+1)`

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Prove the following identities : (cos^(3)theta+sin^(3)theta)/(costheta+sintheta)+(cos^(3)theta-sin^(3)theta)/(costheta-sintheta)=2

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KUMAR PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Test Your Skills
  1. Express each of the following in terms of trigonometric ratios of ang...

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  2. Express each of the following in terms of trigonometric ratios of ang...

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  3. Prove that : tan 20° tan 35° tan 45° tan 55° tan 70° = 1

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  4. Prove that : (cos80^(@))/(sin10^(@))+cos59^(@)cosec31^(@)=2

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  5. If sin theta = cos (theta-45°), where theta and theta- 45° are acute a...

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  6. Evaluate : ( 1 ) cosec (65° +theta) -sec (25° - theta) - tan (55° + ...

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  7. Express all the other trigonometric ratios of angleA in terms of sin ...

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  8. If sintheta=1/3 find the value of 2cot^(2)theta+2.

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  9. Evaluate : 2(sin^(6)theta+cos^(6)theta)-3(sin^(4)theta+cos^(4)theta)...

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  10. Prove the following identities : sec^(2)theta-cos^(2)theta=sin^(2)th...

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  11. Prove the following identities : ((1+tan^(2)A)cotA)/(cosec^(2)A)=tan...

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  12. Prove the following identities : 1/( sectheta-tantheta)-1/(costheta)...

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  13. Prove the following identities : (sintheta-costheta+1)/(sintheta+cos...

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  14. Prove the following identities : (tanA)/(secA-1)+(tanA)/(secA+1)=2co...

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  15. Prove the following identities : (cottheta+cosectheta-1)/(cottheta-c...

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  16. Prove the following identities : (tantheta+1/(costheta))^(2)+(tanthe...

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  17. Prove the following identities : sqrt((1+sintheta)/(1-sintheta))+sqr...

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  18. Prove the following identities : (1+tan^(2)theta)/(1+cot^(2)theta)=(...

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  19. Prove the following identities : (cos^(3)theta+sin^(3)theta)/(costhe...

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  20. If tan theta +sin theta = p and tan theta-sin theta = q, prove that p^...

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