If #13sectheta - 5tantheta =13# then the value of #13tantheta - 5sectheta# can be?

2 Answers
Mar 12, 2017

#pm5#

Explanation:

#{(a/costheta-bsintheta/costheta=a),(-b/costheta+asintheta/costheta=x):}#

after multiplying the first equation by #b# and the second by #a# with posterior add term to term we have

#(a^2-b^2)sintheta/costheta=a b + a x#

after multiplying the first equation by #a# and the second by #b# with posterior add term to term we have

#(a^2-b^2)/costheta=a^2+bx# then

#a b+ax=(a^2+bx)sintheta# so

#{(sintheta=(a(b+x))/(a^2+bx)),(costheta=(a^2-b^2)/(a^2+bx)):}#

but #sin^2theta+cos^2theta=1#

then

#a^2(b+x)^2+(a^2-b^2)^2=(a^2+bx)^2#

solving for #x# we obtain

#x=pmb = pm5#

Mar 12, 2017

Given

#13sectheta-5tantheta=13#

#=>(13sectheta-5tantheta)^2=13^2#

#=>13^2sec^2theta+5^2tan^2theta-2*13*5secthetatantheta=13^2#

#=>13^2(sec^2theta-1)+5^2sec^2theta-5^2-2*13*5secthetatantheta=0#

#=>13^2tan^2theta+5^2sec^2theta-2*(13tantheta)*(5sectheta)=5^2#

#=>(13tantheta-5sectheta)^2=5^2#

#=>(13tantheta-5sectheta)=pm5#