prove that :cos^2 A + sin^2 A.cos 2B = cos^2 B + sin^2 ß.cos2A
Answers
Step-by-step explanation:
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Step-by-step explanation:
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L.H.S=cos
2
A+cos
2
B−2cosAcosBcos(A+B)
=cos
2
A+cos
2
B−2cosAcosB(cosAcosB−sinAsinB)
=cos
2
A+cos
2
B−2cos
2
Acos
2
B+2cosAsinAcosBsinB
R.H.S=sin
2
(A+B)
=(sin(A+B))
2
=(sinAcosB+cosAsinB)
2
=sin
2
Acos
2
B+cos
2
Asin
2
B+2sinAcosAsinBcosB
=(1−cos
2
A)cos
2
B+cos
2
A−cos
2
Acos
2
B
=cos
2
B−cos
2
A+cos
2
B+cos
2
A−cos
2
Acos
2
B.
=cos
2
A+cos
2
B−2cos
2
Acos
2
B+2cosAsinAcosBSinB
Hence,
L.H.S=R.H.S