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Prove that : sec alpha+ sec (120^(@)+...

Prove that :
`sec alpha+ sec (120^(@)+ alpha) sec (120^(@)-alpha)=-3 sec 3 alpha`

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Prove that, cos alpha + cos(120^(@) + alpha) + cos (120^(@) - alpha) = 0

Prove that sin alpha + sin (120^(@) + alpha) + sin(240^(@)+ alpha)=0

Prove that cos alpha cos (120^(@) + alpha) cos (240^(@) + alpha) = 1/4 cos 3 alpha

Prove that, sin^(2) alpha + sin^(2) (120^(@) - alpha) + sin^(2) (120^(@) + alpha) = 3/2

Show that: sin^(3) alpha + sin^(3) (120^(@) + alpha) + sin^(3) (240^(@) + alpha)= - 3/4 sin 3 alpha

Prove that, cos^(3) alpha + cos^(3) (120^(@) + alpha) + cos^(3) (240^(@) + alpha) = 3/4 cos 3 alpha

Prove that : "cosec" alpha+ "cosec" ((2pi)/(3)+alpha) +"cosec" ((pi)/(3)+alpha)= 2 "cosec" 3alpha

Show that, cos^(2)alpha + cos^(2) (120^(@) - alpha) + cos^(2) (120^(@) + alpha) = 3/2.

Prove that cos^2alpha+cos^2(120^@-alpha)+cos^2(120^@+alpha)=3/2

If alpha_1 , alpha_2, ......, alpha_n are in A.P, whose common difference is d , show that sin d [ sec alpha_1 sec alpha_2 + sec alpha_2 sec alpha_3 +.......+ sec alpha_(n - 1) sec alpha_n] = tan alpha_n - tan alpha_1

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-TRIGONOMETRY
  1. If cos alpha+ cos beta= a sin alpha+ sin beta=b, then show that "ta...

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  2. Determine the value of k for which x-1 is a factor of (x^2 +1)+(x+k)do...

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  3. Prove that : sec alpha+ sec (120^(@)+ alpha) sec (120^(@)-alpha)=-3...

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  4. Prove that : "cosec" alpha+ "cosec" ((2pi)/(3)+alpha) +"cosec" ((pi)...

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  5. find the differtiation of tan(a^x)

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  6. If alpha, beta, gamma are positive acute angles, prove that sin alpha+...

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  7. find the differtiation of sin(e^x)

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  8. If cos alpha+ cos beta= a and sin alpha+ sin beta =b, then show that s...

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  9. Find "sin" (A)/(2) and "cos" (A)/(2) in terms of "tan"( A)/(4).

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  10. If tan theta (cos alpha+ sin beta), then show that one value of "tan" ...

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  11. If sin (pi cot theta)= cos (pi tan theta) and n is an integer, then...

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  12. Prove that the maximum value of (cos alpha(1)) (cos alpha(2))...( cos ...

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  13. Show that sin^(2) 12^(@)+ sin ^(2)21^(@)+ sin ^(2)39^(@)+ sin^(2)48^(@...

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  14. If alpha+ beta=(pi)/(2) and beta+ gamma= alpha then prove that tan alp...

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  15. theta and theta(2) are two distinct values of theta[ 0 le theta(1) 2p...

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  16. Find the values of alpha and beta[ 0 lt alpha, beta lt (pi)/(2)] satis...

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  17. Find all the values of alpha for which the equation sin ^(4) x+ cos^(4...

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  18. In sin alpha+ sin beta=(1)/(2) and cos alpha+ cos beta =(5)/(4), find ...

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  19. A 12 cm long wire is bent to form a triangle with one of its angles as...

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  20. If (cos alpha+ cos beta+ cos gamma)/( cos (alpha+ beta+ gamma))=(sin a...

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