Question

If cosθ + secθ = 4 then the value of cos²θ + sec²θ is 

(A) 12 

(B) 13 

(C) 14 

(D) 16

Answer 1

Correct option is (C) 14

\(\cos\theta + \sec\theta = 4\)

Squaring both sides

\((\cos\theta + \sec\theta)^2 = (4)^2\)

\(\cos^2\theta + \sec^2 \theta + 2\cos \theta \sec \theta = 16\)

\(\cos^2\theta + \sec^2 \theta + 2\cos \theta \times \frac 1{\cos \theta}= 16\)    \(\left[ \because \sec \theta = \frac 1{\cos \theta}\right]\)

\(\cos^2\theta + \sec^2 \theta = 16 - 2\)

\(\cos^2\theta + \sec^2 \theta = 14\)