Question

cos^{2}a+cos^{2}a*cot^{2}α=cot^{2}a

Answer 1

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Your answer is....



$= { \cos }^{2} \alpha + { \cos }^{2} \alpha \times { \cot}^{2} \alpha \\ \\ = { \cos }^{2} \alpha + { \cos }^{2} \alpha \times \frac{ { \cos }^{2} \alpha }{{ \sin }^{2} \alpha } \\ \\ = \frac{ { \cos }^{2} \alpha \times { \sin }^{2} \alpha + { \cos }^{2} \alpha \times { \cos }^{2} \alpha }{ { \sin }^{2} \alpha } \\ \\ = \frac{ { \cos }^{2} \alpha \times ({ \sin }^{2} \alpha + { \cos }^{2} \alpha )}{ { \sin }^{2} \alpha } \\ \\ = \frac{{ \cos }^{2} \alpha \times 1}{ { \sin }^{2} \alpha } \\ \\ = { \cot }^{2} \alpha$


Hope it helps ♥

Answer 2

taking lhs
=cos^2A+cos^2A*cot^2A
=cos^2A(1+cot^2A)
we know that 
1+cot^2A=cosec^2A
then
=cos^2A(cosec^2A)
we know that
cosec^2A=1/sin^2A
then
=cos^2A/sin^2A
=cot^2A   = rhs
hence proved

     ;hope this ans would be helpful