Question

If 3cotA=4, check whether 1-tan`A/1+Tan`A=cos`A-Sin`A or not​

Answer 1

Answer:3cot A=4

TanA=1/4/3

=3/4...............1

Cosec^2=1+cot^2

=1+(4/3)^2

=1+16/9

=9+16/9

=25/9

Cosec^2 A=25/9

Degree of cosec goes that side and becomes root

CosecA=root of 25/9

=5/3

CosecA=3/9..............2

CosecA=1/sin theta

5/3=1/sin theta

5sin theta =3

Sin theta =3/5..............3

Cos^2 theta=1-sin^2

=q-(3/5)^2

=1-9/25

=25-9/25

=16/25

Cos^2=16/25

Square of cos becomes root on other side

Cos theta =root of 16/25

Cos theta =4/5.............. 4

=1-tan^2A/1+tan^A

1-(3/4)^2/1+(3/4)^2

=1-9/16/1+9/16

=16-9/16/16+9/16

=16-9/16+9

=7/25

Cos^2A-sin^2A

(4/5)^2-(3/5)^2

=16/25-9/25

16-9/25

=7/25

Therefore

LHS=RHS

Step-by-step explanation: