RRB NTPC Mains or Stage 2 Model Paper 7 with solutions

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Question : 19 of 120

Marks: +1, -0

If q be a positive acute angle satisfying

cos2 θ+ cos4θ q = 1,

then the value of

tan^2 θ+ tan^4 θ

is

$3/ 2$
1
$1/ 2$
0

Solution:

(b) Given,

cos^2 θ+ cos^4 θ= 1

or,

cos^4θ = 1 – cos^2 θ

[∵ sin^2 θ+ cos^2 q = θ]

cos^4 θ= sin^2 θ.

or, 1 =

sin^2 θ/cos^2θ .1/cos^2θ

⇒tan^2θ sec^2 θ =1

or, tan^2 θ. (1 + tan^2θ) = 1

[∵ sec^2θ – tan^2 θ =1]

or, tan^2θ + tan^4 θ=1

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