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Express sin 6theta+sin3theta as a produc...

Express `sin 6theta+sin3theta` as a product.

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To express \( \sin 6\theta + \sin 3\theta \) as a product, we can use the formula for the sum of sines: \[ \sin a + \sin b = 2 \sin\left(\frac{a + b}{2}\right) \cos\left(\frac{a - b}{2}\right) \] ### Step-by-step Solution: ...
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MAHAVEER PUBLICATION-TRIGONOMETRIC RATIOS-QUESTION BANK
  1. If A+B+C=pi, prove that: "sin" A+"sin" B-"sin" C=4 "sin"(A)/(2)"sin...

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  2. If A+B+C=pi and cos A=cos B. cosC,prove that cot B cot C=1/2

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  3. Express sin 6theta+sin3theta as a product.

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  4. Evaluate using multiple angle formula: sin15^@

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  5. Evaluate using multiple angle formula: cos15^@

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  6. Evaluate using multiple angle formula: tan15^@

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  7. Prove that :(tan69^0+t a n 66^0)/(1-t a n 69^0t a n\ 66^0)=-1

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  8. Prove that: (cos 11^0+"sin"11^0)/(cos 11^0-"sin"11^0)=t a n 56^0

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  9. Prove that (cos 8^(@) - sin 8^(@))/(cos 8^(@) + sin 8^(@)) = tan 3...

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  10. Prove that: cos 80^0+cos 40^0-cos 20^0=0

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  11. Prove that:cos420^@ sin390^@+ sin(-300^@)cos(-330^@)=1

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  12. Prove that: ("sin"(A-B))/(s in A s in B)+("sin"(B-C))/(s in B s in C)+...

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  13. Prove that: (sin(A+B)+"sin"(A-B))/(cos(A+B)+"cos"(A-B))=t a n A

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  14. (sinA+sin3A)/(cosA+cos3A)=tan2A

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  15. Prove that: (sinA+sinB)/(sinA-sinB) = tan(A+B)/(2). Cot(A-B)/(2)

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  16. Prove that (cosx +cosy)^2+(sinx+siny)^2=4cos^2((x-y)/2)

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  17. Solve for theta,(0^@ le theta le 360^@) 2sin^2theta+3 costheta=0

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  18. Solve for theta,(0^@ le theta le 360^@) cos theta +sqrt3 sin theta=0

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  19. Find the principal and general solutions of the equation sin x=sqrt3/2

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  20. Find the principal and general solutions of the equation tan x=-1/sqrt...

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