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Find all the values of alpha for which t...

Find all the values of `alpha` for which the equation `sin ^(4) x+ cos^(4)x+ sin 2x +alpha=0` is valid.

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The correct Answer is:
`-(3)/(2) le alpha le (1)/(2)`
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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-TRIGONOMETRY
  1. theta and theta(2) are two distinct values of theta[ 0 le theta(1) 2p...

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

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

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

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

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

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  7. If a tan x+ b tan y+ c tan z=m, then show that the minimum value of ta...

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  8. Prove thattan (alpha+ (pi)/(3)) tan (alpha-(pi)/(3))+ tan alpha tan (a...

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  9. If sin alpha+ sin gamma+ sin alpha sin beta sin gamma=0, show that cos...

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  10. If cos alpha+ cos beta+ cos gamma + cos alpha cos beta cos gamma=0, sh...

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  11. Given the product p of sines of the angles of a triangle and the pro...

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  12. If 0 lt x lt pi and sin x+ sin^(2) x+ sin^(3)x=1, find the minimu valu...

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  13. If 0 le theta lt (pi)/(2) and cos theta+ cos^(2) theta+ cos^(3) theta=...

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  14. If p sin (alpha+ beta)= cos (alpha-beta), then show that (1)/(1- p si...

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  15. If (x)/(a) cos theta+(y)/(b) sin theta=1 and x sin theta- y cos theta=...

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  16. If cot x=(a+a^(3)+a^(3))^((1)/(2)), cot y=(1+ a+ a^(-1))^((1)/(2)) and...

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  17. Show that : (1)/(cos alpha- cos3 alpha)+(1)/(cos alpha- cos5 alpha)+...

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  18. If cos alpha=(sin y)/(sinx), cos beta= (sinz)/(sin x) and cos (alpha- ...

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  19. Show that the value of (tan x+ 2 tan2x)/(tanx) cannot lie within 1 and...

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  20. If alpha+ beta=(pi)/(3)(alpha gt 0 , beta gt 0) find the maximum value...

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