Question

sintheta-costheta+1/sintheta+costheta-1=1/sec theta-tan theta

Answer 1

Step-by-step explanation:

We use sin^2(x)+cos^2(x)=1 for the proof

Explanation:

Writing the Right-Hand side as

1/cos(x)+sin(x)/cos(x)=(1+sin(x))/cos(x)

and now by cross multiplication we get

(sin(x)-cos(x)+1)cos(x)=sin(x)cos(x)-cos^2(x)+cos(x)

and

(sin(x)+cos(x)-1)(1+sin(x))=

sin(x)+cos(x)-1+sin^2(x)+sin(x)cos(x)-sin(x)

Both sides are equal if

sin^2(x)+cos^2(x)=1