prove that (sinA-sin3A+sin5A-sin7A/cosA-cos3A+cos5A-cos7A)=cot2A
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Answer: cot2A
Step-by-step explanation:
sinA-sin3A+sin5A-sin7A/cosA-cos3A-cos5A+cos7A
= -(sin7A-sinA)+sin5A-sin3A/cos7A+cosA-(cos5A+cos3A)
= -2cos4A*sin3A+2cos4A*sinA/2cos4A*cos3A-2cos4A*cosA
= 2cos4A(sinA-sin3A)/2cos4A(cos3A-cosA)
= sinA-sin3A/cos3A-cosA
= -2sinA*cos2A/-2sinA*sin2A
= cos2A/sin2A
= cot2A
= R.H.S
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