Question

solve sec theta minus 1 equal to root 2 minus 1 tan theta​

Answer 1

Answer:  

secθ−1=(√2–1)tanθ

⇒sec²θ+1−2secθ =(2+1−2√2)tan²θ

⇒sec²θ+1−2secθ =3(sec²θ−1)−2√2(sec²θ−1)

⇒sec²θ−3sec²θ+2√2 sec²θ+1+3−2√2-2secθ=0

⇒−2sec²θ+2√2sec²θ+4−2√2−2secθ=0

⇒(2√2−2)sec²θ−2secθ+4−2√2=0

⇒(2√2−2)sec²θ−(4−2√2)secθ −(2√2−2)secθ+(4−2√2)=0

⇒(2√2−2)secθ[secθ−1]−(4−2√2)[secθ−1]=0

⇒[secθ−1][(2√2secθ−2secθ−4+2√2)]=0

⇒secθ−1=0, (2√2sec θ−2sec θ−4+2√2)=0

⇒secθ=1,        sec θ(2√2−2)=4−2√2

⇒θ=0,             sec θ=4−2√2/2√2−2

                                = 2−√2/√2-1 × √2+1/2+1

                                =2√2+2−2−√2

                                =√2                              

θ =sec^-1 √2      = π/4