Question

tan^2+1-2tan upon cot^2+1-2cot=tan 2 prove above problem​

Answer 1

SOLUTION :

$\sf \frac{{ \tan}^{2} \theta + 1 - 2 \tan \theta}{ { \cot}^{2} \theta + 1 - 2 \cot \theta}$

$\implies \sf \frac{{( \tan - 1)}^{2} }{ {( \cot \theta - 1)}^{2} }$

$\implies \: \sf \: \frac{ {( \tan \theta - 1)}^{2} }{ ({ \frac{1 - \tan \theta}{ \tan \theta} )}^{2} }$

$\implies \sf \: - { \tan}^{2} \theta$

Answer 2

Answer:

LHS=

(1+tan

2

A)

2

tanA

+

(1+cot

2

A)

2

cotA

(sec

2

A)

2

tanA

+

(cosec

2

A)

2

cotA

=

cos

4

A

1

cosA

sinA

+

sin

4

A

1

sinA

cosA

=sinAcos

3

A+cosAsin

3

A

=sinAcosA[sin

2

A+cos

2

A]

=sinAcosA=RHS

Hence proved.