If \cos\theta+\sec\theta=2, then \cos^{4}\theta+\sec^{4}\theta=

AP ICET 2015 Paper

Question : 122 of 200

Marks: +1, -0

\cosθ+\secθ=2

, then

\cos^{4}θ+\sec^{4}θ=

Solution:

Given :

\cosθ+\secθ=2

⇒\cosθ+1/{\cosθ}=2

⇒\cos^2θ–2\cosθ+1=0

⇒(\cosθ–1)^2=0

⇒\cosθ=1

⇒\secθ=1

∴\cos^4θ+\sec^4θ=1+1=2

Aliter :

\cosθ+\secθ=2

Squaring both sides,

\cos^2θ+\sec^2θ+2\cosθ.\secθ=4

⇒\cos^2θ+\sec^2θ=4-2=2

Squaring again both sides,

\cos^4θ+\sec^4θ+2\cos^2θ.\sec^2θ=4

⇒\cos^4θ+\sec^4θ=4-2=2

Go to Question:

Prev Question

Next Question