sin(B+ A)+ cos(B - A)÷
sin(B - A) + cos(B + A)
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Step-by-step explanation:
=sin(B+A)+cos(B-A)/sin(B-A)+cos(B+A)
=(sinB*cosA + cosB*sinA + cosB*cosA + sinB*sinA)/(sinB*cosA - cosB*sinA + cosB*cosA - sinB*sinA)
= sinB(cosA+sinA)+cosB(sinA+cosA)/sinB(cosA-sinA)+cosB(cosA-sinA)
= (sinB+cosB)*(sinA+cosA)/(sinB+cosB)*(cosA-sinA)
= cosA+sinA/cosA-sinA
= (cosA+sinA/cosA-sinA)*(cosA+sinA/cosA+sinA)
= cos²A+sin²A+2sinA*cosA/cos²A-sin²A
= 1+ sin2A / cos2A
= sec2A + tan2A
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