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If sinA+sinB=a and cosA+cosB=b, show tha...

If sinA+sinB=a and cosA+cosB=b, show that
`cos(A+B) = (b^2-a^2)/(b^2+a^2)`

Text Solution

Verified by Experts

cos(A+B)
=(1-tan^2((A+B)/2)/(1+tan^2((A+B)/2)
= (1-a^2/b^2)/(1+a^2/b^2) = (b^2-a^2)/(b^2+a^2)`
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MBD PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. If sinA+sinB=a and cosA+cosB=b, show that tan(A+B) = (2ab)/(b^2-a^2)

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  2. If sinA+sinB=a and cosA+cosB=b, show that sin(A+B) = (2ab)/(b^2+a^2)

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  3. If sinA+sinB=a and cosA+cosB=b, show that cos(A+B) = (b^2-a^2)/(b^2+...

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  4. Prove the following : (1+sinA-cosA)/(1+sinA+cosA) = tan A//2

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  5. Prove the following : 8sin^4(1/2theta)-8sin^2(1/2theta)+1=cos2theta

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  6. Prove the following : cos^4(pi/8)+cos^4((3pi)/8)+cos^4((5pi)/8)+cos^4(...

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  7. Prove the following : cos^2(alpha/2)(1-2cosalpha)^2+sin^2(alpha/2)(1+2...

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  8. Prove the following : sin20^@.sin40^@.sin60^@.sin80^@ = 3/16

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  9. Prove the following : cos36^@.cos72^@.cos108^@.cos144^@ = 1/16

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  10. Prove the following : cos10^@.cos30^@.cos50^@.cos70^@ = 3/16

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  11. Prove the following : cos20^@.cos40^@.cos60^@.cos80^@ = 1/16

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  12. Prove the following : tan6^@.tan42^@.tan66^@.tan78^@ = 1

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  13. Prove the following : cot7(1/2)^@=sqrt6+sqrt3+sqrt2+2

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  14. Prove the following : cot22(1/2)^@=sqrt2+1

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  15. Prove the following : cot37(1/2)^@=sqrt6-sqrt3-sqrt2+2

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  16. Prove the following : tan37(1/2)^@=sqrt6+sqrt3-sqrt2+2

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  17. Prove the following : cos(pi/16)=1/2 sqrt(2+sqrt(2+sqrt2))

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  18. If sin A=K sin B, prove the tan frac{1}{2}(A-B)=frac{K-1}{K+1 }tan ...

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  19. If a cos(x+a)=b cos(x-a) show that (a+b) tan x=(a-b) cot a

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  20. An angle theta is divided into two parts alpha, beta such that tan alp...

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