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Verify the identity:
sin(A+B)/sin(A-B) = tan(A)+tan(B)/tan(A)-tan(B)

cos( A + B ) = cosAcosB - sinAsinB ;

cos( A + B ) / ( cosAsinB ) = ( cosAcosB - sinAsinB ) / ( cosAsinB ) = ( cosAcosB ) / ( cosAsinB ) - ( sinAsinB ) / ( cosAsinB ) = cosB / sinB - sinA / cosA = cotB - tanA ;

tan²(x) - sin²(x) = sin²(x)/cos²(x) - sin²(x)

… = sin²(x) (1/cos²(x) - 1)

… = sin²(x) (sec²(x) - 1)

… = sin²(x) tan²(x)

Step-by-step explanation:

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step-by-step explanation: