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Simplify the following : (sin (- theta) ...

Simplify the following : `(sin (- theta) tan(180^@ +theta) tan (90^@ +theta))/(cot (90^@-theta)cos (360^@-theta) sin (180^@-theta))` .

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Simplify the following : (cos (360^@-theta) cosec (180^@+ theta) cot (90^@-theta))/(sec (90^@+theta)cos (-theta)) .

Simplify the following : sin(90^@+ theta) tan (270^@ +theta) cot (90^@+theta) cosec (270^@+theta) .

Prove that cos theta+ sin (270^@-theta)- sin (270^@-theta)+ cos (180^@+theta)=0 .

Prove the following identity : (sin theta)/(cot theta+ cosec theta)=2+ (sin theta)/(cot theta- cosec theta) .

Find ‘x’ from the equation : cosec (90^@ -theta) - x sin (90^@- theta) tan (180^@+ theta) = sin (90^@+ theta) .

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

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

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

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

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

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that : sin 105^@ + cos 105^@ = cos 45^@.

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  2. Simplify the following : sin(90^@+ theta) tan (270^@ +theta) cot (90^...

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  3. Simplify the following : (sin (- theta) tan(180^@ +theta) tan (90^@ +t...

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  4. Simplify the following : (cos (360^@-theta) cosec (180^@+ theta) cot (...

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  5. Prove that cos theta+ sin (270^@-theta)- sin (270^@-theta)+ cos (180^@...

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  6. Prove that : (cos(pi+theta)cos(-theta))/(sin (pi-theta) cos (pi/2+ the...

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  7. Prove that : sin^2 frac (pi)(6)+ cos^2 frac(pi)(3)- tan^2 frac(pi)(4)=...

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  8. Prove that: 2sin^2frac (pi)(6)+cosec^2frac (7pi)(6)cos^2frac (pi)(3)=3...

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  9. Prove that: cot^2frac (pi)(6)+cosecfrac (5pi)(6)+3tan^2frac (pi)(6)=6

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  10. Prove that : 2 sin^2 frac (3pi)(4)+ 2cos^2 frac (pi)(4) +2 cos^2 frac...

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  11. Prove that : 3 sin frac (pi)(6) sec frac (pi)(3)-4 sin frac (5pi)(6) c...

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  12. Prove that : (cos(pi+theta)cos(-theta))/(sin (pi-theta) cos (pi/2+ the...

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  13. Prove the following: cos((3pi)/2+x)cos(2pi+x)[cot((3pi)/2-x)+cot(2pi+x...

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  14. Find ‘x’ from the equation : cosec (90^@ -theta) - x sin (90^@- theta)...

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  15. Find ‘x’ from the equation : cosec (90^@ -theta) - x sin (90^@- theta)...

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  16. In any quadrilateral ABCD, prove that: sin (A + B) + sin(C +D)=0.

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  17. Find all the values of theta satisfying 0lt theta lt pi and tan^2 the...

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  18. Find the period of the following function: sin 2x.

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  19. Find the period of the following function: cos 3x.

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  20. Find the period of the following function: tan 2x.

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