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Find the general solutions of each of th...

Find the general solutions of each of the following equations :
(1) `sin x =(sqrt(3))/(2)`
(2) `sec 3x=-2`
(3) `cot 4x=-1`.

Text Solution

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The correct Answer is:
(1) `x=n pi +(-1)^(n)(pi)/(3), n in Z `
(2) `x=(2 n pi)/(3)+- (2pi)/(9), n in Z`
(3) `x=(n pi)/(4)+(3pi)/(16), n pi Z`.
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NAVNEET PUBLICATION - MAHARASHTRA BOARD-TRIGONOMETRIC FUNCTIONS -Examples for Practise
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  3. Find the general solutions of each of the following equations : (1) ...

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  6. Find the general solution : sec^2 2x=1-tan2x

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  8. Find the general solution of : cosx+sinx=1

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  9. Find the general solution of : cosx-sinx=-1

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  10. Find the general solution of : sqrt(3)cosx-sinx=1

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  11. Find the general solution of : 2tanx-cotx+1=0.

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  12. Find the general solution of : cotx+tanx=2cosecx.

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  13. In any triangle ABC prove that: c cos B-bc cos A=a^2-b^2

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  14. In any DeltaABC, prove that (c-bcosA)/(b-c cos A)=(cos B)/(cosC)

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  15. In triangle ABC , prove that (1) a=b cos C+c cos B (2) b=a cos C+c cos...

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  16. In triangle ABC, prove that 2(bc cos A +ac cos B +ab cos C)=a^2+b&2+c^...

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  17. In triangle ABC , prove that (b+c)cos A +(c+a)cos B +(a+b)cos C=a+b+c.

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  18. In a A B C ,\ ifsin^2A+sin^2B=sin^2C , show that the triangle is righ...

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  19. In triangle ABC, prove that a^2sin(B-C)=(b^2-c^2)sinA.

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  20. In triangle ABC, prove that tan((C-A)/(2))=((c-a)/(c+a))cot(B)/(2).

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