The given equation 2cosa.cot2a−6cosa−cot2a=−3 is identity equation.
Solving the above equation,
2cosa.cot2a−6cosa−cot2a=−32cot2a.cosa−cot2a+3−6cosa=0cot2a(2cosa−1)−3(2cosa−1)=0(cot2a−3)(2cosa−1)=0(cota+3)(cota−3)(2cosa−1)=0
Then, we get
cota+3=0..............................1cota−3=0..............................22cosa−1=0................................3
General solution of 1 is a=nπ+65π , 2 is a=nπ+6π and 3 is a=2nπ+3πand a=2nπ+35π.
Thus, the required solution are a=nπ+65π, a=nπ+6π, a=2nπ+3πand a=2nπ+35π.
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