Prove the identity Trigonometry Question

Calculus
Tutor: None Selected Time limit: 1 Day

1+sinx/cosx + cosx/ 1+sinx = 2secx

Apr 2nd, 2015

cosX / (1+ sinX)

multiply this term with (1-sinX) in Numerator and denominator

cosX *(1-sinX)/ (1+sinX )(1-sinX)

= cosX*(1-sinX) / (1-sin^2X)

= cosX*(1-sinx) / cos^2 X   ...... acc. to identity sin^2X + cos^2X = 1   or 1 - sin^2X = cos^2X

now cosX  canel out from numerator and denominator

= (1-sinX) / cosX


now see the problemm

(1 + sinX)/ cosX + cosX(1-sinX)

put the value of cosX(1-sinX)  which is calculated above

(1+sinX) / cosX +  (1-sinX)/cosX

Take LCM cosX

=( 1+sinX + 1- sinX)/ cosX

= 2 / cosX 

and we know that 1/cosX = secX

= 2secX  which is equal to Right Hand Side

so identity estaablished


Apr 2nd, 2015

This was very helpful, thank you!

Apr 2nd, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Apr 2nd, 2015
...
Apr 2nd, 2015
Feb 19th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer