Question

if tan theta equals x then prove that sin 2theta + tan 2theta = 4x/1 - x^4 please quick answer

Answer 1

Hi,

Here I am taking A instead of theta ,

tan A = x ---- ( 1 )

according to Phythagoruas Theorem ,

sin A = x / √( 1 + x² ) ---- ( 2 )

cosA = 1 / √( 1 + x² ) -----( 3 )

sin2A = 2sinAcosA

= 2 × [ x / √(1 + x² )] × [ 1 / √( 1 + x² )

{ since from ( 2 ) and ( 3 ) }

= 2x / ( 1 + x² ) -----( 4 )

tan2A = 2tanA / ( 1 - tan² A )

= 2x / ( 1 - x² ) { from ( 1 ) }


Therefore ,

sin 2A + tan2A

= 2x / ( 1 + x² ) + 2x / ( 1 - x² )

= 2x { ( 1 - x² + 1 + x² ) / [ ( 1 + x² ) ( 1 - x² ) ] }

= 2x { 2 / [ 1² - ( x² )² ] }

= 4x / ( 1 - x⁴ )

Hence proved ,
.

I hope this helps you.

:)

Answer 2

Answer:

4x/1-x⁴

Step-by-step explanation:

The explanation is given above . Your welcome