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