Question

tanA + cotA = 2 cosec 2A​

Answer 1

Answer:

aking LHS,

\tan A +\cot AtanA+cotA

=\frac{\sin A}{\cos A}+\frac{\cos A} {\sin A}=

cosA

sinA

+

sinA

cosA

Taking LCM,

=\frac{\sin^2 A+\cos^2 A}{\cos A\times \sin A}=

cosA×sinA

sin

2

A+cos

2

A

We know, \sin^2 A+\cos^2 A=1sin

2

A+cos

2

A=1

=\frac{1}{\cos A\times \sin A}=

cosA×sinA

1

Multiply and divide by 2,

=\frac{2}{2\cos A\times \sin A}=

2cosA×sinA

2

We know, 2\cos A\times \sin A=\sin 2A2cosA×sinA=sin2A

=\frac{2}{\sin 2A}=

sin2A

2

=2\csc 2A=2csc2A

is maithade se lagana aa jayega

Answer 2

Step-by-step explanation:

tanA+1/tanA=(tan^2A+1)/tanA

=sec^2A/tanA=1/cos^2A *cosA/sinA

=1/sinAcosA=2/2sinAcosA=2/sin2A

=2cosec2A