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

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

Text Solution

Verified by Experts

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

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

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

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

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

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

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