CotA=b/a, value of cosA+sinA/cosA-sinA
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Given, cosA,sinA,cotA are in G.P. then we've,
sin
2
A=cosA.cotA
or, tan
2
A=cosecA
Now multiplying both sides of the above equation by tanA then we get,
or, tan
3
A=secA.....(1).
Now,
tan
6
A−tan
2
A
=(secA)
2
−tan
2
A [ Using (1)]
=sec
2
A−tan
2
A
=1.
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