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Reduce sqrt(3)sintheta-costheta as a sin...

Reduce `sqrt(3)sintheta-costheta` as a single term consisting sine only

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Suppose `f(theta) = sqrt(3) sin theta – cos theta`
On dividing and multiplying by `sqrt(((sqrt(3))^2 + 1^2))` i.e. by 2
`f(theta) = 2((sqrt(3))/2 sin theta – 1/2 cos theta)`
f(theta) = `2(cos (pi/6) sin theta – sin (pi/6) cos theta) `
As we know that, `sin A cos B – cos A sin B = sin (A – B)`
`f(theta) = 2 sin (theta – pi/6) `
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sqrt(3)sintheta-costheta=sqrt(2)

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RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
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  2. Prove that 5costheta+3cos(theta+pi/3)+3 lies between -4a n d10.

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  3. Reduce sqrt(3)sintheta-costheta as a single term consisting sine only

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  4. Express sintheta-costheta\ as cosine of a single expression.

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  15. Write the maximum and minimum values of 3cos x+4sin x+5.

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  16. Write the maximum value of 12 s intheta-9sin^2\ \ thetadot

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  17. If 12 sintheta-9sin^2theta attains its maximum value at theta=alpha , ...

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  18. Write the interval in which the values of 5costheta+3cos(theta+pi/3)+3...

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  19. If tan(A+B)=p\ and tan(A-B)=q then write thea value of tan2Adot

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  20. If (cos(x-y))/(cos(x+y))=m/n , then write the value of tan x tanydot

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