if x= cot A + cos A , y= cot A - cos A ,show that , x^2 - y^2 = 4√xy
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Step-by-step explanation:
x=cotA +cosA,y=cotA-cosA
lhs=x^2-y^2
=(cotA+cosA)^2-(cotA-cosA)^2
=cot^2A +cos^2A+2cotAcosA-cot^2A-cos^2A+2cosAcotA
=4cotAcosA
cotAcosA=√(cos^2Acot^2A)
=√(1-sin^2A)cot^2A
=√cot^2A-sin^2Acot^2A
=√cot^2A-cos^2A
=√(cotA+cosA)(cotA-cosA)
=√xy
x^2-y^2=4cotAcosA=4√xy
lhs=rhs
pls mark my ans as brainiest
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