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Evaluate using multiple angle formula: `cos15^@`

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To evaluate \( \cos 15^\circ \) using the multiple angle formula, we can follow these steps: ### Step 1: Use the Cosine Double Angle Formula The cosine double angle formula states: \[ \cos 2\theta = 2\cos^2 \theta - 1 \] We want to express \( \cos 15^\circ \) in terms of \( \cos 30^\circ \) because \( 15^\circ \) is half of \( 30^\circ \). Thus, we set \( \theta = 15^\circ \), which gives us: ...
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MAHAVEER PUBLICATION-TRIGONOMETRIC RATIOS-QUESTION BANK
  1. Express sin 6theta+sin3theta as a product.

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  2. Evaluate using multiple angle formula: sin15^@

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  3. Evaluate using multiple angle formula: cos15^@

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  4. Evaluate using multiple angle formula: tan15^@

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Find the principal and general solution of s e c x = 2

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  20. Find the principal and general solutions of the equation sec x=-sqrt2

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