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The equaltion a sin x+b cos x=c, where |...

The equaltion a `sin x+b cos x=c,` where `|c|gtsqrt(a^(2)+b^(2))` has

A

a unique solution

B

Infinite no, of solution

C

no solution

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We know that `|a sinx+bcos x|lesqrt(a^(2)+b^(2))"for all" x inR`
`implies|c|le sqrt(a^(2)+b^(2))`
But, `|c|gtsqrt(a^(2)+b^(2))" "["Given"]`
Hence, `a sin x+bcosx=c` does not hold for any `x in R.`
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OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS AND IDENTITIES-Chapter Test
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  3. If sin beta is the GM between sin alpha and cos alpha, then cos 2beta...

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  4. tan^(2pi)/(5)-tan^(pi)/(15)-sqrt(3)tan^(2pi)/(5)tan(pi)/(5) is equal t...

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  5. If sinB=1/5sin(2A+B), then (tan(A+B))/(tanA) is equal to

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  6. (sin7theta+6sin5theta+17sin3theta+12sintheta)/(sin6theta+5sin4theta+12...

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  7. If (cos(theta(1)-theta(2)))/(cos(theta(1)+theta(2)))+(cos(theta(3)+the...

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  8. (1+cos56^(@)+cos58^(@) -cos66^(@))/(cos28^(@)cos29^@sin33^(@)) =

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  9. alpha and beta are acute angles and cos2alpha = (3cos2beta-1)/(3-cos2b...

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  10. If cosectheta=(p+q)/(p-q), then cot(pi/4+theta/2)=

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  11. If sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)=

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  12. If cos(alpha+beta)=(4)/(5) and sin(alpha-beta)=(5)/(13) , where alpha ...

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  13. about to only mathematics

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  14. The value of sum(k=1)^(3) cos^(2)(2k-1)(pi)/(12), is

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  15. If (a^(2)+1)/(2a)=costheta, then (a^(6)+1)/(2a^(3))=

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  16. The greatest integer less than or equal to (1)/(cos 290^(@))+(1)/(sqrt...

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  17. If tan alpha=(1+2^(-x))^(-1), tan beta=(1+2^(x+1))^(-1) then alpha+bet...

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  18. A and B are positive acute angles satisfying the equations 3cos^(2)A...

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  19. If T(n)=cos^(n)theta+sin ^(n)theta, then 2T(6)-3T(4)+1=

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