SSC CHSL Model Paper 13

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Question : 71 of 100

Marks: +1, -0

If sec θ + tan θ =

2 + √5

, then the value of sin θ + cos θ is :

$3/√5$
$√5$
$7/√5$
$1/√5$

Solution:

sec θ + tan θ =

2 + √5

∴ sec θ - tan θ =

1/{√5+2} =√5-2

On adding,

2\sec\θ=2+√5+√5-2

=2√5

⇒\sec\θ=√5

⇒\cos\θ=1/√5

On subtracting,

2\tan\θ=4

⇒\tan\θ=2

∴{\tan\θ}/{\sec\θ}=\sin\θ=2/√5

∴\sin\θ+\cos\θ

=2/√5+1/√5=3/√5

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