Question

Cota -tana =2 cos2a -1/sina cosa

Answer 1

Answer:

Step-by-step explanation:

Lets take the LHS =

(cosA-sinA)+1/(cosA+sinA)-1

taking conjugate

(cosA-sinA)+1/(cosA+sinA)-1 × (cosA+sinA)+1/(cosA+sinA)+1

multiplying we get

=cos2A-sin2A+2cosA+1/2sinAcosA

=cos2A-sin2A+2cosA+sin2A+cos2A/2sinAcosA

on solving we get

=2cos2A+2cosA/2sinAcosA

=cosA+cos2A/sinAcosA

we can alsom write in the form of

cosA/sinAcosA +cos2A/sinAcosA

on solving we get

CosecA+cotA =R.H.S

I hope it helps you ^_^

Answer 2

solution:

Given,

To prove:

Cot-tan =2.cos^2 -1 /sin.cos

proof :

Taking LHS,

Cot-tan =

Cos/sin - sin/cos

=> cos^2-sin^2 /cos.sin [Taking LCM]

we know,

cos^2+ sin^2 = 1

sin^2 = 1 -cos^2

- sin^2 = cos^2 -1

substituting, in previous equ.

cos^2 + cos^2 -1 /sin.cos

=> 2 cos^2 -1 /sin.cos

= RHS

Thanks for reading ........