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Prove that : (1-sin2x)/(1+sin2x)= tan^...

Prove that :
`(1-sin2x)/(1+sin2x)= tan^2 (pi/4-x)`.

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that : (sinx)/(1+cos x)= tan frac (x)(2).

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  2. Prove that : cot 2A= (cot^2 A-1)/(2 cot A).

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  3. Prove that : (1-sin2x)/(1+sin2x)= tan^2 (pi/4-x).

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  4. Find tan 15^@ and hence show that tan 15^@+ cot 15^@ = 4.

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  5. Prove that : tan 75^@+ cot 75^@=4.

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  6. Given cos 45^@=1/sqrt2, find the value of cos 22 1^@/2.

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  7. Prove that : (1+sin 2 theta-cos 2 theta)/(1+sin 2 theta+ cos 2 theta...

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  8. Prove that : 2 tan 2x= (cos x+sinx)/(cos x-sinx)-(cos x- sinx)/(cos ...

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  9. Prove the following: cos 4x = 1 - 8sin^2 x cos^2 x

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  10. Prove that : sin 4A=4 sinA cos^3 A- 4 cosA sin^3 A.

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  11. Prove that : sin3A+ sin 2A- sinA= 4 sinA cos frac (A)(2) cos frac (3...

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  12. Prove that (tan^2 theta)/(tan^2 theta-1)+(cosec^2 theta)/ (sec^2 theta...

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  13. If cos theta =1/2(a+1/a), prove that : 2 cos 2 theta= a^2+1/ a^2.

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  14. If cos theta =1/2(a+1/a), prove that : 2 cos 4 theta= a^4+1/ a^4.

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  15. If 2costheta=x+1/x, prove that 2cos3theta=x^3+1/x^3

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  16. Prove that : 2 cos theta= sqrt (2+ sqrt(2+2 cos 4 theta)).

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  17. Prove that sin A sin(60° - A) sin(60° + A) = 1/4 sin3A

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  18. Prove that : tan A+tan (60^@+A)-tan (60^@-A)=3 tan 3A.

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  19. Prove that : cos^2 A+cos^2 (A+120^@)+ cos^2 (A-120^@)=3/2.

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  20. If tan^2 theta=2 tan^2 phi+1, show that cos 2 theta+ sin^2 phi=0.

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