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tantheta/(1-cottheta)+cottheta/(1-tanthe...

`tantheta/(1-cottheta)+cottheta/(1-tantheta)=1+tantheta+cottheta` .

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Prove the following identities, where the angles involved are acute angles for which the expressions are defined. : (tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+secthetacosectheta .

Prove that cottheta+tantheta=secthetacosectheta .

Prove that (1/costheta-costheta)(1/sintheta-sintheta)=1/(tantheta+cottheta) .

Prove that (sectheta+tantheta)(1-sintheta)=costheta .

Prove that sintheta/(1-costheta)=cosectheta+cottheta .

sqrt((cosectheta+1)/(cosectheta-1))=costheta/(1-sintheta)=(cottheta)/(cosectheta-1) .

tantheta-cottheta=(2sin^2theta-1)/(sinthetacostheta)=(1-2cos^2theta)/(sinthetacostheta .

Prove that (sintheta)/(cottheta+cosectheta)=2+sintheta/(cottheta-cosectheta) .

MBD-INTRODUCTION TO TRIGONOMETRY-EXERCISE
  1. (tanA+secA-1)/(tanA-secA+1)=(1+sinA)/cosA .

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  2. 1/(cosectheta+cottheta)-1/sintheta=1/sintheta-1/(cosectheta-cottheta) ...

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  3. tantheta/(1-cottheta)+cottheta/(1-tantheta)=1+tantheta+cottheta .

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  4. (cosecA)/(cosecA-1)+(cosecA)/(cosecA+1)=2+2tan^2A .

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  5. (tanA-tanB)^2+(1+tanAtanB)^2=sec^2Asec^2B .

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  6. If cosalpha/cosbeta=m and cosalpha/sinbeta=n then Show that (m^2+n^2) ...

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  7. If costheta+sintheta=sqrt2costheta ,then show that costheta-sintheta=...

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  8. If tantheta+sintheta=m,tantheta-sintheta=n , then show that m^2-n^2=4s...

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  9. If sectheta= x+1/(4x) , then prove that sectheta+tantheta=2x or 1/(2x)...

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  10. IF sintheta+sin^2theta=1 prove that cos^2theta+cos^4theta=1 .

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  11. Evaluate without using trigonometric tables : cotthetatan(90^@-theta)-...

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  12. Prove that : (1+costheta-sin^2 theta)/(sintheta(1+costheta))=cottheta ...

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  13. If sectheta+tantheta=p , prove that sintheta=(p^2-1)/(p^2+1) .

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  14. If cosectheta-sintheta=l, and sectheta-costheta=m , show that l^2m^2(l...

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  15. Prove that (cosectheta+cottheta)/(cosectheta-cottheta) =((1+costheta)/...

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  16. Prove that (1+tan^2 theta)/(1+cot^2 theta)=((1-tantheta)/(1-cottheta)...

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  17. Prove that cosA/(1-tanA)-(sin^2A)/(cosA-sinA)== sin A + cos A. .

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  18. Prove that sec A (1 -sin A) (sec A + tan A) =1.

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  19. Prove that (sec A + cos A) (sec A - cos A) = tan^2A+sin^2A .

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  20. Prove that (1-tan^2theta)/(cot^2theta-1)=tan^2theta,thetane45^@ .

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