Math, asked by HeyyRohan, 7 months ago


 (\csc( \alpha )  -  \csc( \beta ) ) ^{2}  + ( \sin( \alpha )  -  \sin( \beta ) )^{2}  = 4 \sin^{2}  \frac{ \alpha  -  \beta }{2}

Answers

Answered by abhi569
45

Answer:

There is a correction in your question.

Step-by-step explanation:

alpha = A & beta = B

Here,

=> (cosA - cosB)² + (sinA - sinB)²

=> cos²A + cos²B - 2cosAcosB + sin²A + sin²B - 2sinAsinB

=> (cos²A + sin²A) + (cos²B + sin²B) - 2cosAcosB - 2sinAsinB

=> 1 + 1 - 2cosAcosB - 2sinAsinB

=> 2 - 2(cosAcosB + sinAsinB)

{cosAcosB+sinAsinB=cos(A-B)}

=> 2 - 2cos(A - B)

=> 2(1 - cos(A - B))

{1 - cosx = 2sin²(x/2)}

=> 2(2sin²(A-B)/2}

=> 4sin²(A-B)/2 proved

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