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If tan^2 theta=2 tan^2 phi+1, show that ...

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

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If p tan theta = tan p theta , then show that : (sin^2 p theta)/(sin^2 theta)= (sin p^2)/(1+(p^2-1)sin^2 theta) .

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+varphi)=cos (theta-varphi) .

If tan theta=1/2 and tan phi=1/3 , then the value of (theta + phi) is :

If tan^2 theta=2 tan^2 phi+1 , then which of the following is correct ?

If tan theta =p/q , show that : (p sin theta-q cos theta)/(p sin theta+q cos theta)= (p^2-q^2)/(p^2+q^2) .

If tan theta =a/b , prove that a sin 2 theta+b cos 2 theta=b .

Show that the lines (1-cos theta tan alpha) y^2 -(2cos theta+sin ^2 theta tan alpha )xy +cos theta (cos theta+tan alpha )x^2=0 include an angle alpha between them .

If sin theta= n sin(theta+2 alpha) , show that : tan(theta+ alpha)=(1+n)/(1-n) tan alpha .

If tan theta tan phi=sqrt((a-b)/(a+b)) , prove that a-bcos 2theta)(a-b cos 2phi) is independent of theta and phi .

Prove the following identity : cos^4 theta- sin^4 theta= cos^2 theta-sin^2 theta= 2 cos^2 theta-1=1-2 sin^2 theta .

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that : tan A+tan (60^@+A)-tan (60^@-A)=3 tan 3A.

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

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

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  4. Find sinfrac(x)(2), cosfrac(x)(2) and tanfrac(x)(2) in the following:-...

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  5. Find sinfrac(x)(2), cosfrac(x)(2) and tanfrac(x)(2) in the following:-...

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  6. Find sinfrac(x)(2), cosfrac(x)(2) and tanfrac(x)(2) in the following:-...

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  7. If tan frac (x)(2)= m/n, prove than m sin x+n cos x=n.

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  8. If tan theta =a/b, prove that a sin 2 theta+b cos 2 theta=b.

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  9. Prove that (cos^3 theta -cos 3 theta)/(cos theta)+ (sin^3 theta+sin3 t...

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  10. Evaluate : sin frac (3 pi)(8).

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  11. Evaluate : sin frac (5 pi)(24).

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  12. Evaluate : tan frac (pi)(8).

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  13. Prove that : sin^4 frac (pi)(8)+ sin^4 frac (3pi)(8)+sin^4 frac (5pi)...

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  14. Prove that : sqrt((1-cos frac (5pi)(3))/2) =1/2.

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  15. Prove that : sin^2 6x-sin^2 4x= sin 2x sin 10x.

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  16. Prove the following: cos^2 2x - cos^2 6x = sin 4x sin 8x

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  17. Find sin 7 1^@/2, cos 7 1^@/2 and tan 11 1^@/4.

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  18. Prove that : tan 142 1^@/2 =2+sqrt2-sqrt3-sqrt6.

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  19. If theta be any real, prove that : cos4 theta=1-8 sin^2 theta cos^2 t...

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  20. If theta be any real, prove that : sin5 theta= 5sin theta-20 sin^3 the...

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