How do you solve #2costheta*sintheta-2costheta-sintheta+1=0#?

Question

Solve, by factorising, the equation #2costheta*sintheta-2costheta-sintheta+1=0# for #0<=theta<=pi.#
.

2094 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-22T19:12:34

#theta=pi/2 orpi/3#

Here,

#2costhetasintheta-2costheta-sintheta+1=0#

#=>2costheta(sintheta-1)-1(sintheta-1)=0#

#=>(sintheta-1)(2costheta-1)=0#

#=>sintheta=1 >0 or costheta=1/2 >0#

Now, #0 <= theta <=pi=>I^(st)Quadrant or II^(nd) Quadrant#

#:.sintheta=1=>theta=pi/2#

#and costheta=1/2=>theta=pi/3#

Hence, #theta=pi/2 orpi/3#