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Prove the following: (sin x -sin 3x)/(si...

Prove the following: `(sin x -sin 3x)/(sin^2 x -cos^2 x)= 2sinx`

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove the following : (sin 5x -2sin 3x+sinx)/(cos 5x-cos x)= tan x.

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  2. Prove that: ((sin 7x + sin 5x) + (sin 9x + sin 3x))/((cos7x + cos5x) +...

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  3. Prove the following: (sin x -sin 3x)/(sin^2 x -cos^2 x)= 2sinx

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  4. Prove that: (cos x + cos y)^2 + (sin x -sin y)^2 = 4 cos^2frac (x+y)(2...

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  5. Prove that: (cosx-cosy)^2 +(sinx-siny)^2=4 sin^2frac (x-y)(2)

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  6. Prove the following: cot 4x (sin 5x + sin 3x) = cot x (sin 5x -sin 3x)

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  7. If alpha+beta=pi/2, then the maximum value of cosalpha cos beta is:

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  8. If cos (theta + 2alpha) = m cos theta, prove that : cot alpha = (1+m)/...

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  9. If (sin beta)/(sin(2 alpha+ beta))=m/n, prove that : cot (alpha+ beta)...

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  10. If (sin (theta+alpha))/(cos (theta-alpha))= (1-m)/(1+m), prove that : ...

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  11. Prove that : sin (y + z-x) + sin (z + x-y) + sin (x +y-z)-sin (x+y+z)...

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  12. If cos (A + B) sin (C- D) = cos (A- B) sin (C+D), show that : tan A t...

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  13. Prove that : (sinx)/(1+cos x)= tan frac (x)(2).

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

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

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

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

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

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

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

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