Given: tanθ+secθ=4 ......(1) As we know that, sec2θ−tan2θ=1 ⇒sec2θ−tan2θ=1 ⇒(secθ−tanθ)(secθ+tanθ)=1 By substituting the value of tanθ+secθ=4, in the above equation, we get ⇒secθ−tanθ=1∕4 ......(2) Adding equation (1) and (2), we get ⇒2secθ=17∕4 ⇒secθ=17∕8⇒cosθ=8∕17