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(cosec theta -sin theta) (sec theta - co...

(cosec `theta` -sin `theta`) (sec `theta` - cos `theta`) (tan `theta` + cot `theta`) = 1.

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Prove the following identity : (sec theta-cos theta) (cosec theta-sin theta)=1/(tan theta+ cot theta) .

If A = [(cos theta, sin theta),(-sin theta, cos theta)] and B = [(sin theta, - cos theta), (cos theta, sin theta)] , evaluate A cos theta + B sin theta .

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

Prove that (sin theta- "cosec" theta )(cos theta- sec theta )=(1)/(tan theta + cot theta).

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

Prove that : (sin theta)/(1+cos theta) + (1+cos theta)/(sin theta)= 2 cosec theta .

Verify that [(cos theta, sin theta),(-sin theta, cos theta)] and [(cos theta, - sin theta),(sin theta, cos theta)] are inverse of each other.

Prove the following identity : (sin theta+ sec theta)^2 +(cos theta+ cosec theta)^2= (1+ sec theta cosec theta)^2 .

Let A = [ (cos theta, sin theta),(- sin theta, cos theta)] , then show that A ^(2) = [(cos 2 theta, sin 2 theta),( - sin 2 theta, cos 2 theta)]

MBD-INTRODUCTION TO TRIGONOMETRY-EXERCISE
  1. (sec A - cos A) (cot A + tan A) = tan A sec A.

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  2. sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A .

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  3. (cosec theta -sin theta) (sec theta - cos theta) (tan theta + cot thet...

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  4. (1 + cot A — cosec A) (1 + tan A + sec A) = 2 .

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  5. (sintheta+cosectheta)^2+(costheta+sectheta)^2=tan^2theta+cot^2+7 .

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  6. tan^2theta+cot^2theta+2=sec^2thetacoses^2theta .

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

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  8. (1+sintheta)/(1-sintheta)=1+(2tantheta)/costheta+2tan^2theta .

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  9. Prove tantheta/(sectheta-1)+(tantheta)/(sectheta+1)=2cosectheta .

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  10. (1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/costheta .

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  11. Prove the following identities, where the angles involved are acute an...

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

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  13. (sinA+cosA)/(sinA-cosA)+(sinA-cosA)/(sinA+cosA)=2/(sin^2A-cos^2A)=2/(1...

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  14. (tan^3theta)/(1+tan^2theta)+(cot^3theta)/(1+cot^2theta)=secthetacosect...

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  15. 2sec^2theta-sec^4theta-2cosec^2theta+cosec^4theta=cot^4theta-tan^4thet...

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  16. Prove that (sintheta)/(1+costheta)+(1+costheta)/sintheta=2cosectheta .

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  17. (tanA+secA-1)/(tanA-secA+1)=(1+sinA)/cosA .

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  18. 1/(cosectheta+cottheta)-1/sintheta=1/sintheta-1/(cosectheta-cottheta) ...

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

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

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