SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 86 of 100

Marks: +1, -0

The value of the expression (1 + sec 22° + cot 68°) (1– cosec 22° + tan 68°) is

0
1
–1
2

Solution:

(4) (1 + sec 22° + cot 68°) (1 – cosec 22° + tan 68°) = (1 + sec 22° + tan 22°) (1 – cosec 22° + cot 22°)
[∵ tan (90° – θ) = cotθ; cot (90° – θ) = tanθ]

= (1+ {1}/{\cos 22°}+ {\sin 22°}/{\cos 22°} )

(1- {1}/{\sin 22°}+ {\cos 22°}{\sin 22°} )

= ( {\cos 22°+1+\sin 22°}/{\cos 22°} )

( {\sin 22°-1+\cos 22°}/{\sin 22°} )

= { (\cos 22°+\sin 22°+1 ) (\sin 22°+\cos 22°-1 }/{\sin 22° .\cos 22°}

= { (\sin 22°+\cos 22°)^{2}-1}/{\sin 22° \cos 22°}

= {\sin ^{2} 22°+\cos ^{2} 22°+2 \sin 22°. \cos 22°-1}/{\sin 22°. \cos 22°}

= {1-1+2 \sin 22°. \cos 22°}/{\sin 22°.\cos 22°}=2

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