Question

if 3 cot = 7/8 check whether 1-tan² / 1+ tan²= cos²-sin² or not​

Answer 1

Given, 3cotA=4

sinA=ACBC

cosA=ACAB

tanA=ABBC

cotA=BCAB=3k4k

AB=4k

BC=3k

By pythagoras Theorem we get,

AC2=AB2+BC2

AC2=42+32

AC2=16+9

AC2=25

AC2=25

AC=5k

L.H.S

=1+tan2A1−tan2A

=1+(43)21−(43)2

=1+1691−169

=16+916−9

=257

R.H.S

=cos2A−sin2A

=(54)2−(53)2

=2516−259

=257

Hence,

L.H.S=R.H.S proved.

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