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Prove that: sin^2frac (pi)(6)+cos^2frac ...

Prove that: `sin^2frac (pi)(6)+cos^2frac (pi)(3)-tan^2frac (pi)(4)=-1/2`

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Prove that : sin^2 frac (pi)(6)+ cos^2 frac(pi)(3)- tan^2 frac(pi)(4)=-1/2 .

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

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

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

Prove that : sin^2 frac (pi)(8)+ sin^2 frac (3pi)(8)+ sin^2 frac (5pi)(8)+sin^2 frac (7pi)(8)=2 .

Prove that : 3 cos^2 frac (pi)(4)+ sec frac (2 pi)(3)+ 5 tan^2 frac (pi)(3) = 29/2 .

Prove that : 2 sin^2 frac (3pi)(4)+ 2cos^2 frac (pi)(4) +2 cos^2 frac (pi)(3)= 5/2 .

Prove that : cos^2 frac (pi)(8)+ cos^2 frac (3 pi)(8)+ cos^2 frac (5 pi)(8) + cos^2 frac (7 pi)(8) =2 .

Prove that : sin^4 frac (pi)(8)+ sin^4 frac (3pi)(8)+sin^4 frac (5pi)(8)+sin^4 frac (7pi)(8)=3/2 .

Prove that : 3 sin frac (pi)(6) sec frac (pi)(3)-4 sin frac (5pi)(6) cot frac(pi)(4)=1 .

PSEB-TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Find the values of the trigonometric function:- sin (-(11 pi)/3)

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  2. Find the values of the trigonometric function:- cot (-(15 pi)/4)

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  3. Prove that: sin^2frac (pi)(6)+cos^2frac (pi)(3)-tan^2frac (pi)(4)=-1/2

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

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

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  6. Prove that: 2sin^2frac (3pi)(4)+2cos^2frac(pi)(4)+2sec^2frac (pi)(3)=1...

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  7. Find the value of : sin 75^@

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  8. Find the value of : tan 15^@

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  9. Prove the following: cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)= si...

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  10. Prove the following: (tan(pi/4+x))/(tan(pi/4-x))=((1+tanx)/(1-tanx))^2

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  11. Prove the following: (cos(pi+x)cos(-x))/(sin (pi-x) cos(pi/2+x))=cot^2...

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

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  13. Prove the following: sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n +...

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  14. Prove the following: cos((3pi)/4+x)-cos((3pi)/4-x)=-sqrt2 sinx

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  15. Prove the following: 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. Prove the following: sin2 x + 2 sin 4x + sin 6x = 4 cos^2 x sin 4x

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

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  19. Prove the following: (cos9x -cos5x)/(sin17x-sin3x)=-(sin2x)/(cos10x)

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  20. Prove the following: (sin5x + sin 3x)/(cos5x + cos3x)=tan4x

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